CITY were denied three points by a stoppage time West Ham equaliser as it finished 2-2 in an open game at the Boleyn Stadium.
Robbie Brady pounced on Mark Noble's error to fire in his first goal for the Canaries after nine minutes, but the home side rallied and levelled through Diafra Sakho.
After both teams had seen chances come and go, substitute Nathan Redmond drilled home what looked likely to be the winner seven minutes from the end.
There was one final twist to the tale, however, as Cheikhou Kouyate finished from close-range in the 93rd minute to prevent Alex Neil's team securing a third win of the campaign.
Wes Hoolahan returned after missing out against Liverpool at Anfield, and left-back Martin Olsson started for the first time in the league this season, with Brady pushing ahead to midfield.
Missing out were Redmond, who took his place among the substitutes, and Matt Jarvis, who was ineligible for selection under the terms of his loan from the Hammers.
West Ham made one change from their impressive win at league leaders Manchester City last weekend, with Kouyate picked instead of Pedro Obiang.
City opened up their hosts inside the first minute when Brady battled to the byline and crossed for Cameron Jerome, but he struggled to get any power on his header and Adrian made a comfortable save.
John Ruddy was called into his first stop moments later when Kouyate met Dimitri Payet's free-kick, with both teams' confidence showing from their positive starts to the campaign - but it was City who got the first goal.
Brady was presented with the ball after an uncharacteristic error from West Ham skipper Noble, but the Ireland international still needed to advance with confidence and finish with aplomb.
Neil's were soon dominating their opponents and should have scored again on 19 minutes when Olsson's cross found Jonny Howson, who controlled and set himself up expertly - but rifled his left-footed shot just over the bar.
Jerome then fired into the sidenetting from Brady's pass as the Canaries continued to not allow their opponents a sniff, but the pressure eventually subsided and Slaven Bilic's men grew back into the game.
After Manuel Lanzini wasted one counter-attack, the home team scored from their next venture forward - Payet, the leading provider across Europe's top leagues for Marseille last season, picked out Sakho from the right, leaving the frontman with the simplest of finishes.
The goal changed the flow of the game in West Ham's favour - Lanzini curled a free-kick inches wide of Ruddy's post, and Sakho nearly grabbed a second but hooked his half volley over the bar after City's 'keeper had missed a cross.
By the time the whistle for the break came from Mike Dean, City's players will have been relieved to have the chance to head back into the changing room and regroup after a half of two halves.
HALF-TIME: West Ham United 1-1 Norwich City
Howson forced Adrian into duty five minutes into the restart, with the Portuguese goalkeeper tipping the midfielder's shot over the bar after Hoolahan had picked him out 20 yards from goal.
Sakho was left free in the box up the other end and should have scored when Victor Moses found him with a cross, but Ruddy got himself in the right position to make the save, with the match at this point evenly poised.
City's goalkeeper then got down low to his left to deny Payet after Brady's wayward pass had gifted possession to Sakho, before his opposite number took one to the face in the other penalty area, denying Jerome after Howson's work near the byline.
Dieumerci Mbokani replaced Jerome soon after, with Redmond also entering the contest as Neil looked to change things up with 20 minutes left on the clock.
Neither team could take the bull by the horns but City had improved on their ceding of possession at the end of the first half, and Russell Martin saw his backward header float over from Redmond's cross.
As the home crowd quietened, the Canaries grew in stature, with Brady forcing a fingertip save from Adrian - but the stopper was beaten with seven minutes left.
Redmond picked up possession on the left before dribbling into the box, cutting inside and rifling an unstoppable shot into the far corner for his third strike of the season.
Neil brought on O'Neil for Hoolahan to stifle West Ham in the middle of the park, but despite their best efforts Kouyate pounced in injury time to split the points.
FULL-TIME: West Ham United 2-2 Norwich City
: Diafra Sakho (33), Cheikhou Kouyate (90) - Canaries
: Robbie Brady (9), Nathan Redmond (83)
WEST HAM UNITED
: Adrian, Jenkinson, Tomkins, Reid, Cresswell, Kouyate, Noble (c) (Zarate 85), Lanzini (Carroll 72), Payet, Moses (Obiang 57), Sakho. Subs not used
: Randolph (GK), Collins, Antonio, Jelavic.
: Ruddy; Whittaker, Martin (c), Bassong, Olsson; Howson, Dorrans (Redmond 69), Tettey, Brady; Hoolahan (O'Neil 85); Jerome (Mbokani 64). Subs not used
: Rudd (GK), Wisdom, Grabban, R Bennett.
: Mike Dean