Sadio Mané scores Liverpool’s first goal. They went on to defeat West Brom 2-1 but that was not enough to take them top of the Premier League. Photograph: John Powell/Liverpool FC via Getty Images

Another set-piece goal prevented Liverpool going top of the Premier League for the first time since May 2014, but there was no blot on Jürgen Klopp’s landscape against West Bromwich Albion. Another victory is what counts and another impressive Liverpool attacking display provided it.

Liverpool needed victory by a two-goal margin to replace Arsenal at the summit and they looked well on course thanks to first-half goals from Sadio Mané and Philippe Coutinho, only for Gareth McAuley’s late consolation to leave Klopp’s team as joint-leaders.

In his excitement, the stadium announcer declared Liverpool top for the first time under Klopp on the one-year anniversary of the manager’s first game at Anfield. He was mistaken, but that was a rare error on a night when Liverpool should have won comfortably only to give themselves a nervous finale after failing to deal with a Tony Pulis speciality.

The opening 20 minutes was a test of Anfield’s patience until the stadium erupted in celebration of another exquisite team goal that left Klopp throwing right upper cuts towards the main stand.

Albion were strong and organised as always but there is more to the side that frustrated Liverpool with two Premier League draws last season and they created several promising situations only to enrage their manager with a lax final ball. In one counter Nacer Chadli released Matt Phillips behind the Liverpool defence and into the penalty area with a cute reverse pass. The midfielder opted to square to the unmarked Salomón Rondón rather than take the shot but Dejan Lovren foiled the intention with a vital interception. Liverpool heeded the warning magnificently.

Liverpool’s start had contained unwanted echoes of Monday’s dour goalless draw against Manchester United with wayward passing leaving the front three isolated. Adam Lallana’s return in central midfield resulted in Roberto Firmino occupying the central striking role and Daniel Sturridge dropping to the bench but other than Mané’s tireless work on the right the visitors contained the home side initially. Then a glorious dummy spat out their plans.

The breakthrough arrived from an innocuous source when James Milner played the ball inside for Coutinho from the left-hand touchline deep inside the Liverpool half. The Brazilian, with several opponents at his back, created danger in an instant by feinting to his right and leaving the ball to run on to Emre Can. West Brom were suddenly outnumbered and on the back foot. Can released Roberto Firmino down the left, he floated an inch-perfect cross over the head of Allan Nyom and there was Mané to volley home his fourth Premier League goal of the season from close range. It was another example of the collective threat that Klopp cherishes in his teams, as his manic reaction testified.

Can was inches away from making it two when he stretched to meet Nathaniel Clyne’s inviting low cross from the right but just failed to connect. The two-goal advantage Liverpool required was not long coming, however, as the visiting defence went into meltdown.

Darren Fletcher instigated the problems with an awkward back pass towards Ben Foster that his goalkeeper sliced into the air. The former Manchester United midfielder was beaten by Can in the air as he attempted to clear up the mess and Mané set Coutinho free on the left. Liverpool’s No10 had plenty to do, but with another telling drop of the shoulder he sent Craig Dawson and Gareth McAuley sliding out of the equation and drilled a fine finish inside Foster’s near post.

Lallana’s return helped bring more precision and urgency to the Liverpool midfield and they continued to swamp Albion in the second half. Pulis introduced Chris Brunt for Claudio Yacob and James Morrison for Phillips but the midfield changes were ineffective and Liverpool’s dominance merely increased.

Firmino would have made it three at the end of a flowing counterattack involving Mané and Coutinho, but just as he attempted to clip the ball over Foster McAuley appeared from nowhere with a timely block.

The Albion keeper produced a superb save to claw away a Lovren header that was destined for the top corner from Coutinho’s free-kick. Jonas Olsson, in for the suspended Jonny Evans, then launched himself in the way of Can’s goal-bound shot after the irrepressible Brazilian had broken down the left and cut back invitingly for the Germany international.

Chadli could have given the visitors hope of an unlikely comeback with 20 minutes remaining when Brunt’s corner dropped at his feet but he miscued horribly from 12 yards.

It arrived with nine to play as Albion’s prowess and Liverpool’s vulnerability at set pieces suddenly filled Anfield with anxiety. A Brunt corner from the right resulted in Loris Karius making his first save of the game from McAuley’s back-post header. From the subsequent corner on the left, again taken by Brunt, the visitors’ physical strength overpowered Liverpool’s defence and the ball fell kindly for McAuley to convert with a close-range volley.