The goal was extra special for Zamora who supported West Ham as a schoolboy and was brought up not far from Upton Park.
The defeat was rough justice for the Hammers who created the better openings during the game and showed they can still compete with Premiership opposition, despite suffering relegation from the top flight last season.
Spurs could have opened the scoring after 14 minutes when Bobby Zamora's left-foot drive from the edge of the box flew just past the post.
The home side continued to mount pressure on the West Ham goal and on 28 minutes Robbie Keane weaved his way into the penalty box, but with the goal at his mercy dragged the ball wide of the post.
Despite Tottenham's early dominance, it was the visitors who came closest to breaking the deadlock on 37 minutes.
Jermain Defoe's chip over the top of the home defence fell perfectly for Rob Lee, but the former England midfielder saw his shot come back off the post.
And West Ham came even closer on 65 minutes when Michael Carrick's pass released Defoe clean through on goal.
But the £10million-rated marksman saw his close-range effort beaten out by Kaser Keller in the Tottenham goal.
Keane then had a golden chance to send Tottenham into the fourth round of the competition on 76 minutes when he raced onto a Jonathan Blondel pass, but saw David James produce a superb save.
Despite the game going into extra time, Zamora made up for his earlier miss when he fired Tottenham into the lead on 91 minutes.
The former Brighton man turned Anton Ferdinand inside the box and made no mistake this time drilling the ball past James into the corner of the net.
West Ham could have got themselves back into the game almost instantly when Don Hutchison broke free into the box, only for Keller to produce a stunning save.
And they should have been made to pay just a minute later when Tottenham raced down the other end and substitute Helder Postiga forced another spectacular save from James.
West Ham must have known it was not going to be their night when Neil Mellor's header on 107 minutes looked destined for the back of the net, but Keller somehow managed to finger-tip the ball over the crossbar.