Rafael Benítez spoke, but nobody listened. After orchestrating a 4-2 win over Internazionale on Sunday night, the Napoli manager insisted that he had derived no special pleasure from beating his former club. He dismissed the notion that this victory constituted some kind of personal revenge, saying that he was focused only on his own work and still had lots of good friends with the Nerazzurri. And yet, the headline writers disagreed.

"Benítez's vendetta," screamed the front cover of Monday's edition of Gazzetta dello Sport, and Mimmo Malfitano picked up on the same thread on the pink paper's inside pages. "Revenge is served," he wrote. "[Benítez] will have celebrated internally, while the images of his sacking less than three years ago passed through his thoughts."

Technically speaking, Benítez was not actually fired by Inter in December 2010, leaving the club by mutual consent after just six months in charge. He had instigated that parting of ways himself, issuing an ultimatum to the club's then owner, Massimo Moratti, after winning the Club World Cup.

"There are three possibilities," Benítez famously said. "One is to give 100% support to the coach and buy four or five players to build a stronger team, with competition among the players, in order to keep on winning matches and trophies. Two, carry on like this without a project, without planning … The third is to speak to my agent and reach an agreement."

Inter chose the final option, Moratti's previous inclination to support Benítez through a poor start to his first Serie A campaign washed away by the owner's anger at how his manager had undermined a moment of great celebration. A compensation package was agreed and the Spaniard disappeared for what would become a two-year sabbatical from the game.

Opinions differed on Benítez's brief spell at Inter. Many criticised him for his tactical rigidity and questioned his man-management skills amid reports that he had fallen out with senior players. Certainly there were none at the club who would "kill and die" for him, as Wesley Sneijder famously promised to do for José Mourinho.

But others recognised that the manager had walked into an impossible situation, taking over a team that had just achieved something unprecedented – becoming the first Italian side ever to win the treble of Serie A, Coppa Italia and Champions League. Any changes he made were destined to be compared unfavourably with the ones made by his predecessor. If he made none, he would be accused of having no ideas of his own.

Inter's fans in the Curva Nord acknowledged such difficult circumstances with a banner at their first home game after his exit. It read: "Benítez: a sincere thank you from us, the only ones who always supported you." Those fans might have felt some mixed emotions after seeing him appointed by Napoli in the summer. The vacancy had only come up, after all, when Inter hired the Partenopei's existing manager, Walter Mazzarri. The Napoli owner, Aurelio De Laurentiis, spun it into a PR coup, making constant references to the "international dimension" Benítez would bring, and comparing him favourably with his predecessor.

Perhaps he was right to do so. It has been suggested that Benítez's presence was key to the arrivals of big-name players such as Gonzalo Higuaín and José Callejón this summer – although the €100m burning a hole in De Laurentiis's pocket following Napoli's sale of Edinson Cavani and qualification for the Champions League also had something to do with it.

But there were conflicting sentiments for Napoli's fans, too, as Mazzarri returned to San Paolo on Sunday. This was, after all, the manager who had steered them back into Europe's top club competition for the first time in two decades, taking over a team that were lingering in the bottom-half of Serie A in late 2009 and leading them to sixth-, third-, fifth- and then second-place finishes.

Fans in the Curva B lauded him before kick-off, with a banner that read: "Mazzarri … without ink you wrote a determined and emotional film. Those who understood the ending, still applaud you today." Supporters in the Curva A took a different tack, calling him "a coward" for walking out on them. There were both whistles and applause when he stepped out on to the pitch before kick-off.

This day, though, belonged to his successor. Before Napoli's futile Champions League win over Arsenal on Wednesday, Benítez had once again been accused of tactical naivety, journalists arguing that his commitment to attacking football was costing the team points. The Partenopei had won just one of their past four league games, conceding nine goals along the way. Why not subtract one forward, adapting his 4-2-3-1 into a 4-3-2-1 that would provide better cover in midfield?

Benítez responded defiantly on Sunday by fielding just about the most attacking lineup at his disposal, with Lorenzo Insigne, Dries Mertens and Callejón playing behind Higuaín up front. He was rewarded with three goals before half-time against Inter's frail back line.

First Higuaín volleyed home after a poor clearance by Yuto Nagatomo, before Mertens rifled in a brilliant drive from the edge of the penalty area at the end of a sensational one-touch passing move. An almost identical shot from the Belgian two minutes later was blocked by Inter's Samir Handanovic before Blerim Dzemaili prodded home the rebound.

The visitors found the net twice in that frantic first half, too – Esteban Cambiasso and Nagatomo each capitalising on some fine creative work by their team-mate Fredy Guarín. But hopes of an Inter comeback seemed to slip away when Ricky Álvarez was sent off for a second yellow card in the 71st minute. Callejón put the result beyond doubt not long afterwards, before Napoli's Goran Pandev, formerly of Inter, had a penalty (which Insigne was supposed to take) saved in injury time.

This was an important victory for Napoli, whose recent form had cost them ground in the title race. They remain eight points behind the league leaders, Juventus, but this win at least allowed them to put pressure on second-placed Roma, who play Milan on Monday night.

It also helped Napoli to move on at the end of an emotional week, in which they became the first team ever to collect 12 points in the Champions League's group stage and still fail to make it through to the last 16. Higuaín's tears at full-time reflected how much he and his colleagues had invested emotionally in that competition.

Napoli intend to get back into the Champions League next year, and for that reason, too, this weekend's win was important. Inter had begun the weekend just four points behind in fourth place. "It was important to extend our advantage," said Benítez. "They are a direct rival and who were nipping at our heels in the standings."

On the subject of revenge, he would not be drawn. But there was one question about his former club that he could not ignore. Asked if it was true that he had insisted on having pictures of Mourinho taken down from the walls at Inter's Appiano Gentile training facility back in 2010, Benítez responded firmly in the negative – calling such reports "a big lie".

He resisted the temptation to go further, to say more where it did not need to be said. After a win such as this one, he knew it was best just to let the headlines speak for themselves.

Talking points

• Eight league wins in a row now for Juventus, who clobbered Sassuolo 4-0 with the help of a Carlos Tevez hat-trick. It will not be enough to flush away the disappointment of their midweek loss to Galatasaray and subsequent elimination from the Champions League, but such form is certainly looking ominous for their league rivals. And while Sassuolo might not be the toughest opponents in the division, it is worth remembering that the promoted side had drawn away to Napoli and Roma. Oh, and Juve have not conceded a single goal in this current winning run.

• Tevez still has a way to go if he wants to catch Giuseppe Rossi at the top of the scorers' charts. The Fiorentina forward took his league tally to 13 goals this season – three more than the Argentinian – with a beautiful chip over Gianluca Curci to cap the Viola's 3-0 win over Bologna. He provided the assist for a rather nice goal by Borja Valero, too. Rossi insists he does not care for personal accolades. "I'm only interested in helping the team to get into the Champions League places," he said.

• Torino's ascent continued on Sunday with an impressive 2-0 win away to Udinese, a result that seems to have provoked some soul-searching on the part of their beaten opponents. "In a country where nobody ever steps aside, I am able to do it," said the Udinese manager, Francesco Guidolin, in one post-match interview, before adding in another: "I am suffering a lot. If I am the one responsible for this situation, then I am ready to take a step back." Unsurprisingly, it did not take long for the club's sporting director, Christian Giaretta, and owner Giampaolo Pozzo to throw their support behind Guidolin. They know full well how important he has been in keeping this team successful up to now despite a business model that requires the constant sales of star players.

• Lazio finally remembered how to win, Miroslav Klose scoring twice as the Biancocelesti beat Livorno 2-0 at home – their first Serie A victory since October. Will it be enough to save Vladimir Petkovic's job as manager? Only time will tell. The team owner, Claudio Lotito, suggested after the loss to Napoli at the beginning of this month that the manager had three games to prove himself. So far he has lost one (against Torino) and won another, leaving next week's game away to Verona as a potential decider – on paper at least.

Results: Catania 0-0 Verona, Chievo 0-1 Sampdoria, Fiorentina 3-0 Bologna, Genoa 1-1 Atalanta, Juventus 4-0 Sassuolo, Lazio 2-0 Livorno, Napoli 4-2 Inter, Parma 0-0 Cagliari, Udinese 0-2 Torino.

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