The 2-1 victory at Old Trafford was United's fourth in a row at the start of a campaign and took their average points haul in Matchweek 1 to 2.12 per season, with 18 wins from their 27 opening fixtures.
Saints have won only two of 20 Matchweek 1 fixtures, both of which came on the road.
Current PL clubs on Matchweek 1
*The 2011/12 opening-day fixture between Spurs and Everton was postponed
Man Utd's victory was Mourinho's ninth as manager on the opening weekend of a Premier League season, stretching his unbeaten run to 10 matches.
Best managers in Matchweek 1*
*Minimum nine matches in charge on opening weekend