But they left it late, as struggling Coventry capitulated inside the final quarter of an hour under the weight of Richard Shaw's own goal, Teddy Sheringham's penalty and Bobby Zamora's injury-time header.
Following a winless five-game streak, successive away day victories at Wigan Athletic and Burnley had already put unchanged West Ham firmly back on track.
But City – just two points clear of safety – had also mustered back-to-back wins over Brighton & Hove Albion and Nottingham Forest, and with Isaac Osbourne and Shaw returning in place of Steve Staunton and Stephen Hughes, they almost drew first blood.
For when Richard Duffy tried his luck from 25 yards on the quarter-hour mark, the stretching James Walker did well to divert the angled, dipping long-ranger out from under his right-hand angle.
In reply, Sheringham's deft chip was gratefully held by Luke Steele who then clawed away Marlon Harewood's 18-yarder midway through the half.
As West Ham started to edge ahead on points Sheringham's unplayable low cross into the danger zone only needed a touch off Mark Noble's heel, while Shaw denied Harewood in the act of shooting.
It was City who finished the opening period the strongest, though, and seconds before the break, the exposed Walker produced a fantastic stop to deny the breaking Gary McSheffrey.
Seconds after the restart, Walker had to be at his very best again to claw away Rob Page's point-blank header, before Steele showed equal agility to brilliantly steer Anton Ferdinand's downward header around his right-hand post.
And when half-time substitute Matthew Etherington swung over the consequent corner, the Sky Blues' keeper beat down Shaun Newton's sizzling volley only for Noble to hook the loose ball over the top.
With Etherington certainly adding a more incisive edge down the left, West Ham were indeed looking most likely to score and as City defended for their lives Duffy, Page, Marcus Hall and McSheffrey all went in referee Iain Williamson's book alongside the Hammers' dissenting Elliott Ward.
But just when it looked like being one of those frustrating days for the Eastenders, Pardew's side finally got a match-turning stroke of luck.
First, Etherington drilled in a low, 75th-minute centre from the left wing, which saw the unfortunate, diving Shaw power a diving header beyond his own keeper to give Hammers the lead.
Then with three minutes remaining, Sheringham bagged his 21st goal of the season with a twice-taken penalty after Duffy upended Etherington in full flight.
And with West Ham finishing like an express train, Etherington's injury-time cross to the far post was met by unmarked substitute Zamora who planted a firm headed past the helpless Steele to round off a thrilling finale.