"That was a big game for us and we did the job today," said a buoyant Alan Pardew after seeing his side head back up into sixth place and the play-off zone.
"We've had a horrible few days but my young players did everything I asked of them. The pressure on us right now is immense but we've shown we can deal with it and we certainly haven't given up our promotion ambitions."
Without a goal in the previous three games, Pardew had made five changes from the side that had plummeted out of the play-off places following the Bank Holiday defeat at Palace.
But as West Ham's three-pronged attack of Zamora, Connolly and Marlon Harewood struggled to find any service, it was Coventry who made all the early running.
Twice the towering Calum Davenport went close with far post headers, while Gary McSheffrey sent a dipping 25-yarder inches over and Stephen Warnock's thunderous effort from similar range was held at the second attempt by the relieved Stephen Bywater.
Apart from being forced to hold Steve Lomas' low, 18th-minute, 20-yard shot, City keeper Scott Shearer had been a virtual spectator.
Ten minutes before the break, though, he found himself picking the ball out of his net after Adam Nowland's corner was only half-cleared to Hayden Mullins whose return header over the advancing City defence enabled the unmarked Zamora to claim his fifth goal of the season, by firing Hammers into an interval lead with a low, angled ten-yarder.
That was rough justice on the Sky Blues who could have fallen yet further behind on 51 minutes when Christian Dailly met another Nowland corner which Bjarni Gudjonsson headed out from under the crossbar before Connolly acrobatically hooked the loose ball high over.
West Ham had an equally lucky escape shortly afterwards when top scorer McSheffrey's simple low cross was spilled by the red-faced Bywater to a similarly embarrassed Julian Joachim who scuffed wide from all of two yards.
And on 71 minutes, eagle-eyed assistant referee Mr Tingey extinguished the Midlanders' fire when he flagged for Steve Staunton's tug on Zamora, leaving Connolly to despatch a low, no-nonsense penalty to Shearer's right to seal that vital victory for the Hammers.
"It didn't happen for us today," conceded Highfield Road boss Eric Black after seeing his team's outside chances of making the play-offs evaporate into the Upton Park air with this fifth successive away defeat.
"We missed three or four chances and then conceded a goal. We weren't outplayed, but unfortunately we didn't score and so we lost the game."