Former West Ham apprentice Darren Currie worked hard for Town and had the home side's best chance, but buried his volley in Jimmy Walker's midriff, instead of the back of the net.
The game got off to a surprisingly quiet start after Saturday's explosive 2-2 draw at Upton Park, but Currie had his great chance on 12 minutes when Jason De Vos flicked on a Fabian Wilnis long throw, but his shot was too close to Walker.
Hammers danger-man Matt Etherington then got clear down the left, but Kelvin Davis parried his low drive and Richard Naylor cleared the loose ball.
Zamora then got on the end of a Chris Powell cross, but his weak effort was easy for Davis, but surprisingly few chances were being created at this point.
Naylor and Anton Ferdinand glanced headers wide from corners at either end, before the already-booked Ian Westlake was fortunate to stay on after tripping Nigel Reo-Coker as he looked to race clear.
Walker almost made a huge blunder on 36 minutes when Currie tried a speculative shot from 35 yards which swerved late - the keeper just getting enough on it to knock the ball over.
Wilnis almost turned a dangerous low Tomas Repka cross into his own net just after the interval before Davis got down well to field low drives from Reo-Coker and Zamora.
Town felt they had a good shout for a penalty on 58 minutes when Ferdinand nudged Darren Bent just inside the box, but Premiership referee Steve Dunn said no.
Three minutes later West Ham went ahead when Marlon Harewood beat Matt Richards for pace and crossed low for Zamora to tap in from a couple of yards.
Town huffed and puffed before West Ham made it 2-0 on 72 minutes with their next attack, Harewood's floated cross superbly guided home on the volley by Zamora.
Sub Dean Bowditch got on the end of a superb Currie throughball on 78 minutes with a great first touch, but he lost control with his second and it bobbled behind.
Bowditch also had a shot deflected narrowly wide with five minutes to go while Bent guided a header wide when he really should have scored from a pinpoint Richards cross in stoppage time.
West Ham, who brought on Christian Dailly and Mark Noble and left Harewood up on his own towards the end, were happy to soak up the pressure on one of those nights when it looked as if Ipswich would never score.
So it proved and now the much-criticised Alan Pardew is a possible 90 minutes away from a return to the Premiership, and the chance to atone for last year's defeat to Crystal Palace in Cardiff.
As for Ipswich, they have now fallen at this stage in six of their seven play-off appearances, and must now brace themselves to lose key players like Bent and Davis before the new campaign begins in August.