The Seagulls secured promotion to the Premier League on Monday and went into tonight's match knowing that victory would be enough to crown them champions above Newcastle United, but two unfortunate own goals from luckless goalkeeper David Stockdale saw the visitors denied in unlikely fashion.
The hosts had the best early chance, though, when Jonny Howson's low delivery almost picked out Nelson Oliveira at the back post only for the Portuguese striker to fall just short of getting enough on the ball.
Norwich's opening goal arrived after just 18 minutes when Alex Pritchard unleashed a thunderous half-volley from the edge of the box that crashed against the crossbar before bouncing off the back of a helpless Stockdale and creeping over the line.
Brighton were struggling to get into the rhythm that had seen them climb to the top of the table, but John Ruddy was still the busier of the two goalkeepers and he was needed to keep out a glancing header from Hunemeier shortly before the half-hour mark.
Brighton boss Chris Hughton - making his first return to Carrow Road since being sacked by Norwich in 2014 - would have been forgiven for thinking that it was not going to be his side's day when they conceded a second with just six minutes to go until half time.
It arrived in almost identical fashion to the first too, with another Pritchard strike this time striking the post before bouncing back against Stockdale and over the line once again.
Norwich reached the halfway stage with a two-goal lead despite failing to have a single shot on target in the opening 45 minutes, and luck continued to be on their side in the second half when Howson was in the right place to clear Murphy's header off the line shortly before the hour mark.
The visitors continued to press for a way back into the match, but efforts from Murphy and Glenn Murray failed to seriously worry Ruddy in the Norwich goal and the Canaries were able to hold out for a win which puts them a big step closer to securing a top-half finish this season, despite failing to muster a single shot on target during the game.
Brighton, meanwhile, will now renew their bid for a fourth league title in the space of 16 years when they host Bristol City next Saturday.