The door is starting to creak open for Manchester City. Liverpool, with the weight of history threatening to pin them down, found their title charge losing further momentum on an evening of suffocating tension. Even the gift of an offside goal was not enough to extinguish the nerves choking the Premier League’s pacesetters, heightening the impression that Jurgen Klopp’s red machine is finally showing signs of wear and tear.

This was the second successive game Liverpool were gripped by stage fright, with their anxiety captured by the moment when Divock Origi fluffed a glorious opportunity to steal the points with the final kick of a fraught contest. Time stood still when Naby Keïta’s lofted pass fooled West Ham’s stubborn back four and the stage seemed set for Origi, on as a late substitute, to repeat the stoppage-time heroics that won the Merseyside derby two months ago.

The striker’s weak effort went straight at Lukasz Fabianski and means Liverpool’s lead over City stands at three points, presenting the champions with an opportunity to go top when they visit Everton on Wednesday night.

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City can smell blood in the water. Once again Liverpool failed to master mid-table opposition, following up last week’s home draw against Leicester with another laboured display, and they were fortunate to leave east London with a point.

West Ham, bright and inventive in possession, were entitled to feel that they deserved to win. It spoke volumes that Manuel Pellegrini expressed disappointment at the draw.

West Ham defended with impressive organisation, made the clearer chances and were aggrieved with the officials for failing to spot that James Milner was at least a yard offside during the move that culminated in Sadio Mané putting Liverpool in front midway through the first half.

Evidence of City’s silky swagger returning during their win over Arsenal on Sunday had raised the stakes before Liverpool’s latest assignment and there were hints that the visitors were feeling the pressure during a difficult opening period. West Ham flew forward from the first whistle, with Felipe Anderson eager to test out Milner’s nous at right-back, and the hosts looked more than capable of coping without the injured Marko Arnautovic leading their attack.

Although West Ham are drifting in mid-table and out of the FA Cup after a dismal defeat by AFC Wimbledon, they played with the handbrake off. Javier Hernández stung Alisson from long range and the little Mexican ought to have scored after twisting past Virgil van Dijk in the third minute, only to bend his shot inches wide.

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After a while Liverpool found some poise, remembering perhaps that they had scored 16 goals in their previous four meetings with West Ham. Making his fourth league start of the season, Adam Lallana created the danger with a lovely pass into space down the right. West Ham appealed in vain for a flag as the ball reached Milner. He crossed for Mané, who spun Issa Diop and fired past Fabianski.

How the travelling fans roared, sensing lift-off. Yet there have been signs of vulnerability from Liverpool’s defence in recent weeks and West Ham reeled them in with a clever free-kick routine in the 28th minute. With their opponents waiting for a cross, Anderson and Robert Snodgrass combined to release Michail Antonio, who held off Keïta before leaving Alisson rooted to the spot with a firm shot.

Liverpool suffered without the leadership of Jordan Henderson and energy of Georginio Wijnaldum in midfield, where Keïta struggled to assert himself against Declan Rice and Mark Noble, and West Ham should have led at the break. Another free-kick from Anderson deserved a sharper finish from Rice, who was aghast to put his free header over.

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These are the occasions when elite players prove their class. The contest had become a test of Liverpool’s mettle and they needed more from Mohamed Salah in the second half, but the Egyptian found it tough to shake off Cresswell, West Ham’s diligent left-back. Instead it was Anderson who was threatening, always demanding the ball, always willing to run at defenders, luring Joël Matip into a clumsy foul with a piece of skill that left the centre-back looking dizzy.

Liverpool started to rush their passes. Team-mates glared at each other after snatched decisions in the final third. With the minutes ticking away and emotions rising, hope flared when Salah wriggled through on the right and made to shape one of those trademark curling shots into the far corner, but it was too close to Fabianski. It was beginning to feel like one of those nights.

Quick guide Premier League title race: the remaining fixtures Show Hide Manchester City (86 points) 24 Apr Man Utd (a)

28 Apr Burnley (a)

4 May Leicester (h)

12 May Brighton (a) Liverpool (85 points) 21 Apr Cardiff (a)

26 Apr Huddersfield (h)

5 May Newcastle (a)

12 May Wolves (h)

Klopp argued that injuries have disrupted Liverpool’s rhythm, pointing out that Milner had missed four days of training with a virus. Van Dijk also looked leggy in central defence and Trent Alexander-Arnold’s return from a knee injury cannot come soon enough. Liverpool need the right-back’s youthful enterprise and quality deliveries.

They had run out of ideas long before the end. West Ham protected Fabianski’s goal with impressive organisation, with Rice so perceptive in his screening role, and they went closest to forcing a second goal, Noble’s volley flying narrowly over.

When it was over Klopp held an agitated conversation with Pellegrini on the touchline. There was no doubt which manager was feeling more relaxed about life.