Jürgen Klopp’s dream of winning every remaining league game may not be idle fantasy after all if his side can come up with this sort of quality on a regular basis. Liverpool certainly got the unlikely project off to an auspicious start with a comprehensive victory over Tottenham, keeping up their unbeaten record against other top-six Premier League teams in the process and winning their first league game of 2017 in some style.

Klopp said he wanted his players to produce a performance to make Anfield smile, and they did just that, though it always helps when Liverpool can name all four of their leading attackers – Philippe Coutinho, Roberto Firmino, Adam Lallana and Sadio Mané – in the same team. It does not always work, the quartet appeared in the unexpected defeat at Hull last week, but here Liverpool’s energetic running was causing Spurs problems from the off and Mané in particular looked unplayable at times. The Senegal international had the chance to join Spurs in the summer but the club felt his wage demands were too high. Perhaps it was no accident that he chose this game to show his true worth.

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Liverpool started like a team determined to make an early impression, and might have scored before Mané gave them the lead had not Coutinho’s goalbound shot struck the trailing heel of Toby Alderweireld. Tottenham were holding a high defensive line and giving the home side space to run into, which is exactly what happened when a visiting attack broke down and Georginio Wijnaldum was able to slip Mané into an almost empty Spurs half a couple of minutes later. After holding off what remained of the Spurs defence Mané only had Hugo Lloris to beat, which he did deftly enough despite appearing to lose his footing in the act of shooting.

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If that was an ideal start for a side short on confidence, it got better with a second goal within a matter of just over a minute. This time a ponderous Eric Dier was caught in possession by Mané, who probably imagined either Firmino or Lallana would put the ball in the net, only for both Liverpool players to be denied by excellent saves from Lloris. The danger was not cleared, however, and when the ball came back in his direction Mané scored at the third attempt.

Playing centre-half in Jan Vertonghen’s absence, Dier did make some amends by getting across to stop Mané’s run into the penalty area after half an hour, though by that stage the Liverpool player could already have completed a hat-trick. He hit the side-netting from a decent opportunity midway through the first half, then followed up on Liverpool’s next attack to bring another diving save from Lloris.

Liverpool also had centre-half problems, Lucas Leiva standing in because Dejan Lovren was injured and Ragnar Klavan sick, though in the first half Tottenham were unable to put the home back line under any sustained pressure. It was Liverpool finding all the space and creating all the chances, and Coutinho really should have put them further ahead when he took his time with a clear shooting opportunity and still ended up putting the ball too close to Lloris.

It was not quite one-way traffic: Son Heung-min brought a save from Simon Mignolet before the interval and Christian Eriksen was too high with a free-kick from the edge of the area. However, Harry Kane and Dele Alli were not featuring in as many Spurs attacks as Mauricio Pochettino would have liked and neither were the full backs providing the usual width and penetration.

Liverpool ended the first half as they had started it, swarming all around the Spurs box, and they should probably have had greater reward for their movement and invention than a couple of corners that came to nothing.

At times the home side were passing for fun inside the area, and though their enterprise was a pleasure to watch, Klopp would almost certainly have preferred a little more directness and a third goal to reflect their overall superiority.

The closest Spurs came to mounting a comeback in the second half was when Kane hit a post from an offside position. Their frustration began to show after an hour, with Alli and Kane both fouling Nathaniel Clyne in quick succession, the latter receiving a caution for an unnecessary stamp.

When Emre Can was sent on for the last few minutes, Dier welcomed him with an uncompromising challenge that also brought a booking. Alderweireld became the fifth Spurs player booked when he brought down Firmino as he raced into the area, with the visitors in danger of losing their composure in the closing stages.

Liverpool were unable to add another goal but they remain on top of the imaginary mini-league comprising the top-six teams. Despite ending Chelsea’s unbeaten run, it is Spurs, lucky to claim a point at the Etihad last month, who now appear to be struggling to impose themselves on top-six rivals.