Vladimir Petkovic embraced the madness. Not for him the route of Zdenek Zeman and the many other coaches who have, in years gone by, sought to play down the significance of the Rome derby, claiming that this was just a game like all the rest. Speaking to the press on Saturday, Lazio's coach took the opposite tack. Although he had never experienced it first-hand, he knew that: "This match is different".

In so many ways he would be proved correct. Before it had even kicked off Sunday's match had already fallen outside of the norm, for the way fans and players of both teams came together inside the stadium to commemorate the fifth anniversary of the death of the Lazio supporter Gabriele Sandri – shot dead by a policeman on 11 November 2007 – even while others were fighting outside.

Amid violent clashes at least one fan was reported stabbed, while a Molotov cocktail was thrown at police. Against that backdrop it will have been easy for Petkovic to understand the team's mascot, Olimpia the eagle, is not allowed to fly her customary pre-match lap of the stadium before the derby.

Not all of the unique features of this day were so foreseeable, nor necessarily linked to the football in any direct way. But if the dramatic downpour which converted the playing surface into a paddling pool could have happened on any other afternoon, then the sudden shutting down of the stadium's floodlights five minutes after kick-off felt immediately like one of those moments that somehow belonged to derby lore.

"Lotito, pay the light bill," crowed the Roma fans inside the stadium – invoking the Lazio owner Claudio Lotito whose repeated financial disputes with the stadium's operators over the past few years have led him to threaten to move his team's European games elsewhere. A section of the home support soon joined in the chant.

Both sets of fans held up lighters and mobile phones to compensate. Neither they, nor the players, wanted the game stopped, though the referee Gianluca Rocchi insisted on waiting until at least some of the floodlights had been restored before agreeing that they could continue. Under such a deluge, visibility remained poor.

Within moments of play resuming, Lazio would fall behind. Erik Lamela appeared to push Senad Lulic as he raced in to direct a fine header past Federico Marchetti, but no foul was awarded. For the Argentinian it was a remarkable sixth goal in as many games, as well as his eighth of the season – enough to place him alongside Edinson Cavani and Stephan El Shaarawy as Serie A's leading goalscorers.

At that point the picture might have looked bleak for a Lazio team whose recent domestic form had been far from ideal. In the three-and-a-half games since Miroslav Klose put them 3-0 up at home to Milan on 20 October, the Biancocelesti had conceded nine goals and scored only one.

But where Petkovic had encouraged his team to treat this match "like a final", Zeman had called on his team to play their usual game. That might seem like sound advice were it not for the fact that Roma's standard approach this season has typically involved throwing away a lead.

That was precisely what they proceeded to do at the Stadio Olimpico. Ten minutes before the break, Antonio Candreva's 30-yard free-kick – firmly struck but essentially straight down the middle of the goal – somehow eluded Roma's Mauro Goicoechea. For a Lazio team who had hardly been peppering the keeper, it was a huge and timely boost.

Before half-time they would take the lead, Klose seizing on a Hernanes cross-shot which was slowing to a halt on the wet surface before the German lashed it home from six yards out. Worse was soon to come for Roma, Daniele De Rossi sent off for punching Stefano Mauri in first-half injury time.

Herein, perhaps, the reason that Zeman had been so keen to play down the tensions ahead of this fixture. The manager had at last bowed to popular sentiment, restoring De Rossi to the centre of midfield and positioning him as the team's regista just in front of the defence, but he was well aware that the player was prone to letting his emotions take hold in such games.

"For two days we had been speaking about these risks, saying that we needed not to react to any provocations," Zeman said afterwards. "The derby is of course a game that you feel intensely, but when you feel it too much then you pay."

It was not emotion, but straightforward bad defending that cost Roma the third goal, Iván Piris heading a long ball straight into the path of Mauri, who advanced one step from the edge of the area before dispatching it past Goicoechea. The Lazio captain was later sent off himself for a second booking. Miralem Pjanic then pulled a goal back for Roma from a 40-yard free-kick but his team had left it too late to find an equaliser.

At full-time Lazio's players ran to celebrate under the Curva Nord, where they were even eventually joined by Olimpia the eagle (not that all of the players looked so thrilled with that development). "We are going to enjoy the moment," said Petkovic. "It was important for me to win my first derby. It's among the strongest emotions I've ever felt."

His players seemed similarly moved. "I'm living a dream. From the first day that I've been here I have been hoping this moment would arrive," said Candreva – with the club since January. Klose, asked about his goal, replied: "I don't care about that at all. The important thing was just to win … it is a very important win for the fans and the club."

This was a third successive derby win for Lazio, but while that might be the most important thing to fans, the most impressive aspect four outsiders is that such a result sits naturally within the context of what Petkovic has achieved so far. A full-time charity worker as recently as 2008, Petkovic arrived at the club with extremely limited experience but great confidence and impressive tactical savvy.

Reputed as an attack-minded coach, many had expected him to impose the 3-4-3 he had used with former teams upon his new charges but rather than force square pegs into round holes he instead came up with a new 4-1-4-1 that took best advantage of the players at his disposal. Hernanes, formerly deployed just behind the attack, has been moved back to a deeper-lying role from which his productivity has greatly increased.

With victory Lazio have extended their advantage over Roma to five points. The picture might look rather different were the Giallorossi capable of finishing games as strongly as they start them. Zeman's team have dropped 14 points this season from winning positions – the most of any team in the division.

The mood among supporters – so overwhelmingly positive when the manager arrived – might just be beginning to turn. Franco Baldini's suggestion last week that Roma would listen to offers for De Rossi has hardly helped to raise spirits. He attempted to play those comments down on Sunday, insisting that: "We have neither the necessity nor a desire to sell him. I just said that we will consider any offers, that is part of my job."

Baldini also absolved De Rossi of blame for his sending off, blaming the tensions of the derby. The midfielder had gone to apologise to Mauri in the Lazio changing room at full-time, a gesture that was well received. Zeman, was a little less forgiving. "He started well, but that act condemns him. I am sad for him and the team, as we have to play without him for the next two games."

And though the club also continue to publicly stand behind their manager, the constant repetition of the same mistakes can only be a cause for concern. "Zeman is truly a dreamer," wrote Massimo Mauro in La Repubblica. "Always the same football, always the same defeats, and yet he never takes a step back."

It is doubtful that Sunday's result will prompt him to rethink his methods. But it might just prompt one or two fans to rethink a manager who has won the derby only once in seven attempts across his two stints as manager of Roma.

Talking points

• De Rossi's red card not only means a suspension from Roma, but effectively also from the national side - the midfielder was omitted from Cesare Prandelli's Italy side to face France this week as a punishment for his actions which are in breach of the national team's code of conduct. You can see the full squad here.

• Following the end of their unbeaten run, it took Juventus all of a week to restore their four-point advantage at the top of Serie A. A 6-1 demolition of Pescara on Saturday was followed a day later by news that second-placed Internazionale had lost away to Atalanta – ending their own runs of consecutive wins and away wins at 10 each.

• Paul Pogba was not part of that win over Pescara – dropped from the matchday squad as a punishment for twice showing up late to training. The player has since apologised to the manager, and the club have downplayed the incident. In the meantime he has also been left out of the France squad to face Italy – a game for which many had speculated he might receive his first call-up.

• Another week, another tremendous win for Fiorentina, who overturned Milan at San Siro despite the continued absence of Stevan Jovetic. Rumours that the Rossoneri are considering Vincenzo Montella as their next manager were lent fresh fuel by Adriano Galliani's suggestion before the game that "his teams play how the president likes", but at this stage it would be tempting to ask whether the Milan job is really more tempting. After 12 games, Fiorentina sit fourth, three points off second place, despite a fixture list that has already seen them face Inter, Napoli and Milan away, as well as Juventus and Lazio at home. Milan, by contrast, finished the weekend in 13th.

• Montella's team were greeted by hundreds of cheering fans at the train station upon their return to Florence, but a rather different crowd awaited Sampdoria as they landed back at Christopher Columbus airport in Genoa following a 2-0 loss away to Palermo. The team's bright start to the season is a distant memory, and the players were jeered by a group of 50 or so fans as they disembarked, some of whom then attempted to block the team bus from leaving the airport, demanding an audience with the players before they were eventually moved on by police.

Results: Atalanta 3-2 Inter, Cagliari 0-0 Catania, Chievo 2-2 Udinese, Genoa 2-4 Napoli, Lazio 3-2 Roma, Milan 1-3 Fiorentina, Palermo 2-0 Sampdoria, Parma 0-0 Siena, Pescara 1-6 Juventus, Torino 1-0 Bologna.Red ca

The current Serie A table