Eddie Howe’s side took the lead at the Stade Velodrome through a sixth minute goal from in-form winger Harvey Barnes.
Marseille kept pushing, however, and Aubameyang eventually got the equaliser just after half-time, scoring the winner four minutes later.
Speaking to TNT Sport after the game, the former Arsenal, Barcelona, and Chelsea forward admitted he still feels great despite his age.
"I'm very happy to be here at this club to enjoy moments like tonight. It was a great game. We started a bit sloppily, but we reacted well,” he said.
"I'm feeling great, even if I'm 36. When you play these types of games, you want to play more and score more.
"It was very important, especially at home and for the fans. If we want to go through, then we have to win games."