The Premier League has its reminder that Liverpool remain a potent force. Last week’s loss to Manchester City at the Etihad has been exorcised in thrilling fashion, visiting players a blur of movement against panicked opponents whose own encouraging start to the season has been put in proper context. Tottenham Hotspur had shipped five to these rivals last term but, at times, this felt every bit as chastening.

Brendan Rodgers could not have envisaged a more satisfying way to celebrate a century of games in charge, his 56th win in that time matching the records of Bill Shankly and Rafael Benítez. If his team’s progress through their first two fixtures had suggested they were still embroiled in a period of post-Luis Suárez adjustment, then this was them reimposing their credentials. Raheem Sterling was irrepressible, every bit as threatening as he had been last December, while Jordan Henderson swarmed around central midfield and Daniel Sturridge demonstrated he can provide a supply line as well as a finishing touch these days.

They have added Alberto Moreno’s aggression and jet-propelled pace down the left. The full-back was the scorer of a fine goal and was generally far more impressive here than he had been when more pertinently tested at City on Monday. Mario Balotelli, who had drawn the pre-match focus, was hardly required to revel on debut. Yet the reality that Rodgers even coaxed a performance of impressive work-rate from the £16m arrival from Milan also bodes well. Balotelli’s radar was uncharacteristically awry in front of goal but his composure in the six-yard box will return. Liverpool had him defending corners for the first time in his career, and holding up the ball superbly against Younès Kaboul with his back to goal. If he can maintain the industry and eagerness to combine with team-mates that typified his display in little over an hour here Liverpool really will have secured a bargain.

The Italian will add to their options up front, but this was Liverpool rediscovering last season’s zest. They hassled and harried the composure from Spurs here, Mauricio Pochettino’s team denied any time to consider their options on the ball and too often lethargic in chasing back possession once it had been surrendered. They seemed dazed. Dismantling Queens Park Rangers, or even triumphing at West Ham, is all well and good but, when jolted out of their own rhythm, they lacked the nous to recover. “We are a team who are still improving, still learning,” said Pochettino. “We were up against a very good team who almost won the Premier League last season and have built the team for more than two years. But that’s no excuse. We lost this in the key moments of the game.”

They had trailed early, Sturridge teasing space from Jan Vertonghen and Nacer Chadli before liberating Henderson, whose centre was converted neatly by Sterling at the far post. Yet having been spared a second concession by Balotelli’s profligacy – a pair of headers from close range and a miscued volley from distance with Hugo Lloris out of his area which dribbled wide – they should have equalised when Kaboul’s diagonal pass confused Mamadou Sakho and Dejan Lovren to leave Chadli in possession in front of goal. Yet Simon Mignolet saved that attempt and, if that had hinted at a shift in momentum just before the break, the award of a soft penalty to the visitors rather knocked the stuffing from Tottenham’s challenge.

Eric Dier, exposed here for the first time since his summer arrival from Sporting Lisbon, was penalised for a tug back on Joe Allen. “Soft,” claimed Pochettino, though the contact was ill-advised. Steven Gerrard scored his 43rd penalty for the club and Liverpool were not finished there. Pochettino flung on Andros Townsend to chase the game but the winger was dispossessed by Alberto Moreno inside the visitors’ half and pursued the full-back as he seared upfield. There was no catching the Spaniard, his finish from inside the penalty area dispatched crisply inside the far post to settle the contest.

Sterling should have added a fourth after a glorious dribble that left opponents on their knees only for anxiety to grip, indecision choking the finish at a grateful Lloris. “He dribbled through the Spurs defence like Ricky Villa, but his finish was more like Ricky Gervais,” said Rodgers. “But he was exceptional. His tactical awareness is improving, and for a kid of 19 … he’s going to be great, even if he does have to work a bit on that left foot.” Opponents will not always offer him this much space, but Spurs tend to be obliging. Liverpool have now scored 14 times against Tottenham in the last 300 minutes of games between the sides, with the London club having failed to register at all in that period.

They anticipate concluding the signing of Montpellier’s Benjamin Stambouli, a defensive midfielder of considerable promise, on deadline day and he should add to their steel in the centre, with Etienne Capoue in particular having reverted to last year’s rather laboured form here. Others will be moved on, with QPR interested in taking Sandro and Aaron Lennon, and Crystal Palace hoping to sign the left-back Zeki Fryers, most likely on loan. This Spurs team are still learning how to impose the style Pochettino demands, their side very much a work in progress. Liverpool, on this evidence, feel much more like the finished article.

Man of the match Raheem Sterling (Liverpool)