Norwich had contrived to lose a 2-1 lead in the second half but it was they who had the final say, with Hooper firing home his first goal of the season five minutes from the end.
Bruno Saltor put Brighton ahead in the 33rd minute, with Jonny Howson levelling five minutes later for the hosts who led soon after the interval thanks to a superb Russell Martin strike.
Brighton were in the ascendancy once Kazenga LuaLua levelled and Adrian Colunga fired home a penalty, but Hooper ensured Norwich would not be denied, although a late red card for Bradley Johnson meant they finished on a sour note.
The Canaries were looking to get their campaign back on track after successive away defeats had seen them drop to 10th in the table and it took time for them to get into their stride.
They had an early sight of goal when awarded a free-kick just outside the area, but Martin Olsson’s shot was straight at David Stockdale and summed up a low-key opening.
Brighton seemed content to let the game adrift along, although they did go close with a free-kick of their own on the half-hour mark, with Gary Gardner’s shot going just wide.
It was their first decent effort of the game, and the Seagulls proceeded to take the lead from their second purposeful attempt after 33 minutes.
An excellent cross from the right from Colunga picked out Saltor at the back post and the right-back headed cleanly past the exposed John Ruddy.
It took the goal to rouse Norwich from their slumbers and they got back on level terms with a goal of classic simplicity. Nathan Redmond produced some trickery on the right before delivering a perfect ball into the area where Howson was in the right place to head powerfully home.
Boosted by a rare first-half goal, Norwich nearly got a second two minutes before the interval, with Redmond cutting the ball back for Cameron Jerome, whose powerful effort was well blocked.
Howson then fired wastefully over after latching on to a loose ball on the edge of box as a poor half drew to a close.
The hosts got their noses in front in fine style after 49 minutes. A Norwich corner was only partially cleared and fell to Martin 30 yards out. The Norwich captain rifled the ball home into the top corner to mark his 200th match for the club in memorable fashion.
The hosts, who had bossed possession all game, were looking dangerous and went close again five minutes later when Jerome nodded a Redmond cross just over.
Johnson had another glorious opportunity moments later after the Seagulls had carelessly given the ball away, and it took a good save from Stockdale to keep out his crisply struck drive.
Stockdale then foiled Redmond as the Canaries continued to dominate but the hosts were stunned after 66 minutes when Brighton equalised.
Home defenders were guilty of standing off LuaLua when he made his way into a crowded box and, after waiting for the right moment, he simply curled the ball into the far corner.
Norwich responded well, with Stockdale again denying Redmond, but it was Brighton who edged ahead from a penalty after 77 minutes. Colunga was brought down by Jos Hooiveld as he darted into the box and the winger picked himself up to coolly slide the ball home from the spot.
Substitute Hooper equalised after 85 minutes. The former Celtic man had only been on the pitch for seven minutes when he pounced on a loose ball in the box and rifled a low shot past Stockdale.
The drama was not over, with Johnson being dismissed for Norwich in stoppage-time for a second bookable offence when bringing down Greg Halford.