Ronald Koeman's men stunned Old Trafford as they came away with a 1-0 win.
The Saints came away from Old Trafford with a 1-0 win thanks to a late goal from new signing Charlie Austin.
The Dutchman was convinced by the Red Devils' vice-chairman Ed Woodward to remain in charge however, as The Sun reports that Woodward is against the idea of changing the manager midway through the season.
However, there may well be some United fans that were ultimately disappointed that the club's hierarchy decided to convince van Gaal to stay.
As well as their poor recent record - they have lost five of their last ten games in all competitions, with just three wins to speak of during the run - their style of play has come in for criticism.
Against Ronald Koeman's side, the home team managed just one shot on target, which helps explain why the club are the lowest scorers of any side in the top eight of the Premier League.