Roy Keane called Leadbitter from the bench with Sunderland trailing in the 70th minute after Marek Saganowski had put promotion rivals Southampton in front.
Midfielder Leadbitter won the game with a 20-yard pile-driver into the top right-hand corner three minutes from time.
The win put Keane into top spot for the first time in his fledgling managerial career.
Polish striker Saganowski looked to have condemned the Black Cats to their first defeat of 2007 when he fired home his ninth goal in nine starts for Saints in the 67th minute.
Substitute Danny Guthrie fired Djamel Belmadi's centre across the face of goal and Saganowski volleyed past Sunderland goalkeeper Darren Ward from six yards.
Trinidad and Tobago winger Carlos Edwards levelled the scores with a superb solo goal ten minutes later.
Edwards picked the ball up midway inside the Saints half before cutting in from the right and picking out the top left-hand corner from 25 yards.
Sunderland, protecting a 15-match unbeaten League run, had the better of a frantic opening 45 minutes and could have been three up early on.
David Connolly shot against the post in the 14th minute before Southampton goalkeeper Bartosz Bialkowski tipped a Stephen Elliott strike wide.
Manchester United veteran Dwight Yorke should have scored in the 18th minute when he put a free header over the bar from Tobias Hysen's cross.
Leon Best fluffed Southampton's best chance of the first half when he shot straight at Sunderland's keeper Ward from close range, after robbing the day-dreaming Jonny Evans.
Keane showed his ruthless streak by making two half-time changes, hauling off Elliott and the hapless Liam Miller for Dean Whitehead and £1million striker Anthony Stokes.
Yorke wasted another good opening in the 58th minute when he scuffed wide from 12 yards from a Connolly flick.