Graham Potter's team were far from their best and Norwich were dominant for large periods but failed to capitalise on their chances.
Josh Sargent, who was a real handful throughout, missed the two very decent chances while Teemu Puki also chipped one into the side-netting when well placed.
Brighton's best moment arrived when Leo Trossard smacked the bar with a smart volley from 15 yards and Neal Maupay was also denied a decent shout for a penalty when he was clipped in the box by Tim Krul.
Albion were lucky to get away with a point and were grateful for excellent defensive displays from Dan Burn, Shane Duffy and Lewis Dunk.
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