There had been little to choose between the sides in the opening half. West Ham produced some neat passing movements, often instigated by Alex Song or Pedro Obiang from the back of midfield, but there were no clear chances on the end of it, even though John Ruddy did have to help an angled shot on the rise from Enner Valencia pass safely over the bar. Noble created possibly the best West Ham chance to go ahead before half-time, one that was wasted by Valencia's poor control.
Norwich, typically, were full of energetic movement going forward, with Hoolahan coming up with some nice bits of trickery. Yet as with their opponents their build-up play lacked an end product. A couple of shots from distance, by Russell Martin and Jonny Howson, had the home crowd rising from their seats, but both ultimately missed the target.
Given recent form, though, reaching half-time on level terms was a bonus for the home side, who noticeably moved up a gear from the start of the second half.
Almost immediately, Cameron Jerome missed only narrowly with a good bending effort from outside the box and would surely have scored had Hoolahan found him on an unmarked run through the middle after Steven Naismith had dispossessed James Collins. As it was, Norwich went ahead with a goal after 54 minutes.
It stemmed from another West Ham player caught in possession, this time Michail Antonio, robbed by Brady, the Norwich left-back, who immediately found the space to curl a right-foot shot beyond the reach of goalkeeper Adrian and in off the underside of the bar.
Manager Slaven Bilic made a double change after 62 minutes, taking off Valencia and Song, but within three minutes Norwich had punished them with a second goal. West Ham were simply giving the ball away too easily and when another move broke down on the right, Norwich swept forward at pace.
The ball passed to Naismith, cutting in from the right to take a ball from Hoolahan. The former Everton striker's shot was blocked by Collins but spun up and over his head landing at the feet of Hoolahan, who had continued his run, stayed just onside and tucked the ball past Adrian to seemingly put the points in the bag for the home side.
Yet, having scored four goals but leaked five against Liverpool at home last month, Norwich again were not resilient enough to hold on to their lead as West Ham suddenly found fresh legs to storm back, scoring twice in the space of three minutes to stun the Carrow Road.
The first goal on 74 minutes owed everything to the strength and determination of substitute Victor Moses, who launched a powerful run along the inside left channel in which he simply would not be denied, bouncing off two strong tackles, the second of which knocked him off his feet before he scrambled up and forced a save from Ruddy.
The Norwich goalkeeper pushed the ball away firmly but it ran straight to Payet, who had the technique to get his foot over the ball and steer it safely into the net.
West Ham clearly sensed Norwich's nerves now and built more pressure. Andy Carroll, the other half of the double substitution, combined with Moses on the left to find Payet unmarked inside the Norwich box, the Frenchman looking up and rolling a superbly weighted pass for Noble, runing through the middle, to blast the ball home from the edge of the box.
West Ham attacking stats
The closing minutes unfolded almost as a siege of the Norwich box, with those in green and yellow desperately trying to stave off another defeat as West Ham pressed for a winner.
Yet there was almost another twist as Norwich almost stole a decisive goal of their own in the last of the five minutes of time added, when Sam Byram cleared off the West Ham line from Sebastien Bassong.
- Telegraph