Kevin Nolan headed the winning goal as West Ham overcame struggling Coventry to move level on points with Championship leaders Southampton.
Nolan scored on 66 minutes after a George McCartney cross was headed back across goal by James Tomkins.
Coventry goalkeeper Joe Murphy pushed Sam Baldock's shot onto the bar while Mark Noble missed an open goal.
The Sky Blues' Lukas Jutkiewicz headed wide and near the end Carl Baker's deflected shot hit the bar.
It was only the Hammers' second win in six attempts but they are now only being kept off top spot on goal difference by the Saints, who were beaten 3-0 at Brighton.
The visitors created the first opportunity when Gary McSheffrey crossed towards Chris Hussey, whose first-time shot flew narrowly wide.
West Ham were denied by Murphy twice in quick succession, saving from Nolan with his feet and, from the ensuing corner, keeping out Jack Collison's snap-shot.
The hosts were dominating but City were dangerous on the break and Jutkiewicz should have done better with a free header from a Gary Deegan cross that he nodded wide.
At the other end Julien Faubert's volley flew wide and Papa Bouba Diop's header was deflected clear before the interval.
Early in the second half Jutkiewicz squandered another good chance after Faubert made a hash of his clearance.
Jutkiewicz had more time than he realised in the penalty area and headed the ball meekly over the top when he could have allowed the ball to drop to give himself the chance of a shot.
But the City goal was leading a charmed life, with Tomkins heading Noble's corner wide and Baldock also off target from Carlton Cole's cross.
Murphy then produced two stunning saves to force Baldock's shot onto the underside of the crossbar and then palm away a powerful header from Collison.
The loose ball fell to Tomkins but the defender skewed his shot into the ground and it bounced over the top.
The breakthrough eventually came when Tomkins beat Hussey in the air to head McCartney's cross back across goal where Nolan was on hand to nod it past Murphy.
It should have been two minutes before the end after Richard Wood under-hit a backpass but Murphy saved well from Frank Nouble and Noble put the rebound wide with the goal gaping.
And the Hammers' hearts were in their mouths when Baker's shot was deflected onto the crossbar as the hosts survived a nervy ending.
West Ham boss Sam Allardyce: "We were all relieved when we saw it go in because we were all wondering whether it was going to happen for us or not on the basis of how many chances we created and how good their keeper was.
"We've played, very, very well today and the only thing I can criticise the lads for is not winning by more goals. Everything else was fantastic.
"Without a doubt the suspended players being back made all the difference because we saw the quality and how we controlled the game and how often we persisted in pressurising Coventry who finally cracked in the end."
Coventry boss Andy Thorn: "I thought the boys gave me everything. We stuck in there but towards the end it was disappointing to concede the goal, an appalling goal from our point of view.
"But I can't ask for any more effort from them because they were excellent and we could even have nicked something at the end. I thought we finished strongly.
"We stood up to them well and then as it went on I thought we got stronger and we started getting our own chances - and I thought one of them could have gone in for us.
"West Ham are going to be up there. They're well organised and well managed but I was a little bit disappointed that we didn't get anything."