Goals by David Di Michele and top-scorer Carlton Cole made it another horror night for Hull City, who slumped to their sixth successive Premier League defeat and down another rung into tenth place.
Both sides had enjoyed FA Cup fourth round success in the chilly North Sea air on Saturday, as Phil Brown's Tigers saw off the Lions of Millwall at the KC Stadium, while the Hammers won at Hartlepool.
And now with the River Thames providing an equally wintry backdrop for a Premier League clash between two teams heading in different directions, both managers resisted the temptation to start their new £5million signings.
With his side sitting in eighth spot, Zola kept Germany Under-21 striker Savio Nsereko - a recent capture from Serie B outfit Brescia - on the bench until three minutes from time, while Matthew Upson and Lucas Neill were recalled in place of substitutes James Tomkins and Julien Faubert.
A decade ago, former painter and decorator Jimmy Bullard had only got as far as a solitary appearance in the dug-out for West Ham United at Liverpool, before moving on to Peterborough United, Wigan Athletic and Fulham.
And following his recent move from Craven Cottage, the mercurial midfielder again found himself on the bench on his return to Upton Park, where the ninth-placed Tigers made three changes as keeper Matt Duke, Kevin Kilbane and Geovanni replaced Tony Warner and substitutes Peter Halmosi and ex-Hammer, Richard Garcia.
Certainly, Duke was on full alert throughout, as Valon Behrami steered a rising 20-yarder inches over, before Jack Collison saw his low shot turned aside and then Di Michele curled a delightful long-ranger onto the right-hand post.
Midway through the half, the visiting keeper looked in all sorts of trouble, when Sam Ricketts recklessly tugged Cole to the slippery East End turf, but he brilliantly guessed correctly as he dived to his left to deny Mark Noble a third successive penalty with an outstanding one-handed save.
Di Michele was the next to be foiled when Duke produced another fine stop but, by now, Hull were visibly creaking under the weight of Hammers pressure.
Sure enough, on 33 minutes, the keeper's luck ran out when he could only parry Cole's awkward, low, angled shot towards the back post, where Di Michele got in front of Andy Dawson to fire his fourth goal of the season high into the net from close range.
Although, Geovanni, Manucho and Daniel Cousin had forced Robert Green into saves, the first half belonged to Zola's men, who also saw the luckless Collison rap the post, before the helplessly exposed Duke foiled the breaking Cole, to restrict the half-time deficit to that solitary Di Michele strike.
Within five minutes of the restart, however, West Ham did double their lead, when Noble's deep free-kick was nodded back across goal by Upson and, although Di Michele could only rock the woodwork for the third time, Cole was on hand to steer the rebound over the line.
The on-fire striker's tenth goal of the season was the cue for Brown to introduce debutant Bullard and Craig Fagan at the expense of Geovanni and Manucho and, within moments of his arrival, the £5million man sent Green sprawling headlong across goal to divert his low 18-yarder around the base of his right-hand upright.
Sadly for the beleaguered Brown, that was just sporadic resistance against the confidence-laden Hammers, who would have had a hatful of late goals but for the determination of the defiant Duke, who foiled Cole, Di Michele, Noble and Faubert before the final whistle brought his side's miserable night to an end.