Sir Alex Ferguson hailed Javier Hernandez after the Mexican booked United's place in the FA Cup fifth round with the winner at St Mary's.
The striker was on hand to slot home after being well found by Ryan Giggs 14 minutes from time.
The Reds had earlier gone behind to a fine strike from Southampton midfielder Richard Chaplow on the stroke of half-time. Michael Owen levelled proceedings on 65 minutes before Chicharito netted his second goal in as many games.
"He's only had one chance and he's scored - one chance, one goal is a tremendous ratio," the boss told MUTV. "He has great feet in and around the box and gets his shots away quickly with hardly any backlift.
"His workrate is fantastic and he's always on the move. We probably we didn't find enough space for him at times, but you also have to give Southampton a bit of credit too. Their defenders read things well."
Just as at Bloomfield Road on Tuesday night, the Reds struggled to get into their stride in the first period, although the manager admitted afterwards that the formation he opted for simply didn't work.
"Sometimes we make it difficult for ourselves, but in fairness I maybe meddled with the system by trying a diamond in the middle of the pitch," he explained. "Manchester United are used to playing with width and I think that [the system] was a problem for us. It wasn't working at all.
"We had some possession but we never really threatened apart from two or three shots from the edge