Valon Behrami's first goal of the season got West Ham off to a superb start, before top-scorer Carlton Cole netted his ninth of the campaign on the hour and Julien Faubert confirmed all three points with his first-ever strike in English football.
Looking for back-to-back wins for the first time this season, West Ham made two changes from the side that beat Birmingham City last time out as Jonathan Spector and Guillermo Franco came in for the injured Herita Ilunga (back) and substitute Mido.
And the Hammers' determination to get off to a flyer against their fellow strugglers was there for all to see as Alessandro Diamanti whipped in a clever, angled, free-kick that the alert Boaz Myhill clawed out from the base of his near post, with just seconds on the clock.
But Zola did not have to wait much longer to see his side make the vital breakthrough, when Radoslav Kovac robbed Tom Cairney in midfield before finding the barnstorming Behrami who collected his return pass from Franco and slotted a low ten-yarder past the exposed Tigers goalkeeper.
Having taken a third-minute lead, the Hammers pressed forward and Scott Parker, Kovac plus Cole threatened before Diamanti almost decapitated one of his own fans with a wayward far post volley.
Midway through the first half, Behrami scorched his way into the Hull box, where Myhill had to be at his best to beat away the stinging shot from the Switzerland international, who then saw his point-blank header parried.
Coming into this relegation dogfight with only the Hammers' superior goal difference separating these two strugglers, Brown had made just one switch from the team that lost at Blackburn Rovers ten days ago as Amr Zaki replaced the benched Jozy Altidore,
Although Jan Vennegoor of Hesselink and George Boateng forced Robert Green into two fine saves, the toothless Tigers were firmly on the back foot during a first half in which Craig Fagan was booked for pole-axing Parker, while the impressive Franco and Paul McShane tested referee Martin Atkinson's patience to the limit with their tantrums and tangles.
But it was Fagan's collision with Diamanti seven minutes into the second period that was to prove even more costly for the visitors, who were consequently reduced to ten men thanks to the harsh second yellow card that was dished out to the furious Hull wideman.
And West Ham wasted no time making their extra man count as Faubert brilliantly threaded a fabulous 40-yard pass behind Anthony Gardner, to leave Cole with just the exposed Myhill to beat, and the England striker took his season's tally to nine with a confident angled finish.
Diamanti also tried a brilliant Beckham-esque effort from inside his own half that saw the back-pedalling Myhill palm the ball out from under his left-hand angle and the irresistible Italian also curled inches over from a much closer 15 yards.
Midway through the half, Brown had responded with a triple substitution that saw Stephen Hunt, Cairney and Zaki make way for Seyi Olofinjana, Nick Barmby and Altidore but the trio could do nothing to turn the tide for a Hull side, who were then reduced to nine men, when Gardner was stretchered off, after falling awkwardly in a challenge with Matthew Upson.
And two minutes into stoppage time, Faubert compounded a miserable afternoon for hammered Hull, when he collected from Kovac and fired an unstoppable 18-yarder past Myhill to claim his first goal in two-and-a-half seasons at Upton Park.