Having sealed promotion to the Premier League with victory over Wigan Athletic on Monday, Chris Hughton's side - seven points ahead of nearest rival Newcastle United with three games remaining - could have clinched top spot with a win at Carrow Road, but two moments of misfortune for Stockdale denied the league leader.
Alex Pritchard's fine 18th-minute shot struck the crossbar and ricocheted into the net via the helpless Stockdale and, after John Ruddy's smart save had denied Uwe Hunemeier's close-range header at the other end, the Norwich midfielder repeated the trick.
Pritchard, linked with a move to Brighton last year, again hit the woodwork, the post this time deflecting the ball against Stockdale and over the line six minutes before half-time.
Hughton, on his return to his former club, failed to muster a tangible response from the visitors as Norwich held firm and retained a threat on the break after the interval.
Brighton could now see Newcastle close the gap at the top to four points against Preston North End on Monday, before the Seagulls take their title bid back to the Amex Stadium to face Bristol City next weekend.