That was the Barking-born striker's second goal since his January transfer from Spurs and after having seen him squander a handful of earlier chances, it left Alan Pardew declaring: "I was disappointed with Bobby's hold-up play in the first half.
"But after the break he was much better and when he was given his best clear cut chance he kept his head and dispatched it. It was an important win for us."Following their FA Cup capitulation at the hands of Fulham, West Ham were back focusing on the main job in hand - promotion.
And Pardew was given a huge boost by being able to select his best 11. But it was City who started best as Paul Parry forced Stephen Bywater into a low save, before the Hammers keeper then denied Robert Earnshaw with a point-blank stop after the striker was sent clear.
Midway through the half, the Bluebirds had their wings clipped when Rhys Weston was stretchered away with an ankle injury following a robust Nigel Reo-Coker tackle and they should have been reduced to ten men shortly afterwards when Daniel Gabbidon cynically chopped Zamora as he raced away in desperate pursuit of that home debut goal.
David Connelly skied the resulting free-kick high over, while Christian Dailly and Matthew Etherington agonizingly sent efforts across the face of goal before Reo-Coker struck the base of Martyn Margetson's right-hand post in the 40th minute with a low 18-yarder.
While Gabbidon had been lucky to escape with only a yellow card, Tomas Repka was equally fortunate to escape with just a booking - a dirty dozen for the season - after leaning into referee George Cain during a furious injury-time argument, for which Pardew made him apologize at the final whistle.
Just after the restart, Zamora wrapped the Bluebirds' bar before climaxing a clever jag-back with an angled shot that flew across the face of goal.
On the hour, Marlon Harewood saw his 20-yarder parried by Margetson and as the snow started to fall from the freezing East End skies, the Hammers striker's powerful 15-yarder was then brilliantly parried by the keeper.
On 73 minutes, however, Margetson was finally beaten when Zamora sprinted on to a deflection off Connelly and outpaced Chris Barker before slotting a 15-yarder under the exposed keeper to claim a victory that sent his side into a play-off berth.