The French side waited till the last 15 minutes before scoring twice to send the packed Velodrome into ecstasy.
Julien Rodriguez broke the deadlock in the 76th minute, poking home from close range when Samir Nasri’s wonder corner-kick fell into his path after hitting the far post.
Djibril Cisse sealed the win in the injury time when he went face-to-face with the Besiktas goalie and had no difficulty in scoring the second.
The French side top Group A with three points, two ahead of Liverpool and Porto, who settled for a 1-1 draw on the same day.
Porto grabbed the lead as early as the eighth minute from a well-taken penalty by Lucho Gonzalez.
Dutch striker Dirk Kuyt put the visitors level in the 17th minute when he towered to Sami Hyypia’s volley and headed the equalizer home.