While Jose Mourinho's side suffered a fourth straight European defeat at Feyenoord, Saints ran out comfortable winners against last season's quarter-finalists Sparta Prague.
Tonny Vilhena scored the only goal for Giovanni van Bronckhorst's side as they recorded a famous victory over their illustrious English opponents – who were playing their first ever group match in the competition's history.
Mourinho made eight changes from the Manchester derby defeat but his fringe players were unable to produce a performance of merit as they lost for the second game in a row.
Elsewhere in United's group, Zorya were denied victory in their first group game in Uefa competition as Simon Kjaer netted an 90th minute equaliser in Ukraine. Dmytrio Grechyshkin had earlier given the hosts the lead in the second half but they were unable to hang on and take advantage of United's earlier slip-up.
Claude Puel could have no complaints with his much-changed Southampton line-up however, as two first half goals from Charlie Austin and Jay Rodriguez's stoppage time strike saw their second straight continental campaign begin on a winning note. Austin tucked away a penalty after just five minutes before heading home Cuco Martina's cute cross to double the lead, with substitute Rodriguez side-footing home in the second minute of added time.
The shock of the night also came in Group K where Hapoel Beer Sheva overcame three-time winners Inter Milan at the San Siro. Frank de Boer has won just once since being appointed the club's new manager and that record continued as first Miguel Vitor and then Maor Batr Buzaglo netted for the visitors.
Dundalk created history by becoming the first Irish team to earn a European point after coming from behind to grab a late draw with AZ Alkmaar. Stijn Wuytens had opened the scoring and when Stepehn O'Donnell was dismissed the League of Ireland side looked doomed. But Ciaran Kliduff headed home in the 89th minute to spark huge celebrations.
Zenit St Petersburg produced the comeback of matchday one after recovering from 3-0 down to claim victory over Maccabi Tel Aviv in stoppage time. Last season's Israeli Premier League runners-up held a comfortable advantage with 13 minutes left before Aleksandr Okorin, Robert Mak and Giuliano pulled the scores level. Luka Djordjevic then popped up in the fourth minute of added time to claim the most famous of wins.