Saints had threatened to repeat their famous 1976 Wembley win over United when Richard Chaplow gave them a deserved half-time lead against the much-changed Barclays Premier League leaders.
After Guly had headed over from six yards, Chaplow spared his team-mate's blushes moments before half-time when he broke into the United box and slammed the ball into the roof of the net at debutant keeper Anders Lindegaard's near post.
However, as in Tuesday night's dramatic comeback at Blackpool, the introduction of the veteran Ryan Giggs helped change the game, with goals from Michael Owen and Javier Hernandez putting the visitors into the last 16.
The equaliser came in the 65th minute, with Gabriel Obertan's drilled cross deflecting right into the path of Owen, who nodded home his first goal since September.
And United completed their latest comeback 14 minutes from time, Jose Fonte's slip allowing Hernandez to receive Giggs' throughball and steer an improvised finish into the net.