Rickie Lambert opened the scoring for the newly-promoted hosts, before Robin van Persie equalised not long after.
However, Morgan Schneiderlin restored the Saints’ lead after the break and Nigel Adkins’ side looked set for a memorable victory.
Van Persie equalised with three minutes left on the clock, before bagging his hat-trick and the winner in injury time.
Sir Alex Ferguson was pleased to win the match and hailed replacements Paul Scholes and Javier Hernandez for their displays from the bench.
“Van Persie scored a fantastic equaliser for us (to make it 1-1 before the break) and second half you think let’s just get down to business and get this done,” Ferguson told Sky Sports.
“But credit to Southampton they kept loading the ball into the box.
“Everything we did in preparation for the game has all been to deal with back-post crosses and they scored two goals off them so that was disappointing.
“But credit to Southampton they are good at it.
“For that period we were well out of it until Paul Scholes came on the park. His vision and consistency of passing gave us complete control of the game.
“Then it was just a matter of getting the goals of course and Van Persie has come up with them.
“He’s got four goals in two starts and he’ll get better.
“I think Chicharito made a difference too. He started stretching them and making fantastic runs off the ball. I was delighted with his performance,” the legendary Scottish coach revealed.
By Gareth McKnight