Arsenal secured top spot in Group A ahead of PSG while Barcelona's 4-0 win saw them match the 20-goal Champions League group-stage record.
Robert Lewandowski's starred with his sublime free kick as Bayern beat Atletico Madrid to seal their 15th successive Champions League win.
Madrid could set a new club record of 35 unbeaten games by the time they fly to Japan for this year's World Club Cup next week.
Jordan Henderson, Adam Lallana, Roberto Firmino and the rest of the entourage watched on at the Camp Nou as Barca dismantled Gladbach 4-0.
Mauricio Pochettino has played down suggestions that there is a release clause in the contract of defender Toby Alderweireld.