Two Chelsea loanees were among the scorers in the opening fixtures of the Europa League group stage.
Bertrand Traore scored for Ajax in their 2-1 win at nine-man Panathinaikos in a game that saw three red cards.
Baba Rahman grabbed the only goal in Schalke's victory at Nice, for whom ex-Liverpool striker Mario Balotelli failed to add to his two debut goals.
Frank de Boer's Inter Milan - in Southampton's Group K - lost 2-0 at home to Hapoel Be'er Sheva.
Inter, who have won the European Cup and Uefa Cup three times each, have picked up four points from their opening three games in Serie A since De Boer replaced Roberto Mancini.