Robert Green made a similar save to deny Chris Eagles, then after 15 minutes Anthony McNamee fired wide when well placed.
Seven minutes later he tried his luck from a tighter angle and the ball went even further wide of the target.
On the half-hour Dickson Etuhu was only inches away from giving Norwich the lead with a firm header from Simon Charlton's free-kick.
Five minutes later Andrew Hughes hit a bobbling ball over Foster's crossbar.
At the other end Matthew Spring's first time shot from long range rebounded off a post.
A minute before the break Malky Mackay marked his return to Carrow Road by pulling back Paul McVeigh and the referee had no hesitation in giving a penalty.
McVeigh's right-foot shot went straight down the middle with Foster diving to his right to give the Canaries a rather fortunate 1-0 lead.
Watford went close in the dying moments of the first half and two minutes into the second the leveler came when Green could only palm away Marlon King's cross and Darius Henderson's right-foot shot from 12 yards found the net via the post.
This was followed by a spell of intense Watford pressure but Norwich went ahead again when Darren Huckerby crossed from the left and Peter Thorne scored his first goal for the club with a well placed far post header.
Handball by Jurgen Colin gave Watford a free-kick on the edge of the box. Green saved King's low shot but Henderson was quickest to the rebound and smashed the ball into the net from close range.
Huckerby and Jarrett went close to restoring the lead for City. Huckerby then set up Henderson but he failed to make a clean contact with his shot.
At the other end Gary Doherty did well to block King's shot and the game went into injury time with the home side looking to be on top.
But the Hornets provided the sting in tail when Spring capitalised on some indecisive defending by City and scored with a crisp right-foot shot into the bottom corner past Green's despairing dive.