Benjamin Bourigeaud scored a hat-trick for Rennes, including a pair of penalties, but goals from Luka Jovic and Rafael Leao ensured Milan were never really in danger of blowing a 3-0 lead from the first leg.
Benfica also saw off French opposition as a 0-0 draw away to Toulouse was enough to send the Portuguese side through following their 2-1 victory in last week's first leg in Lisbon.
Marseille host Shakhtar Donetsk later in Jean-Louis Gasset's first match at the helm following the exit of Gennaro Gattuso. The tie is level at 2-2 after the opening match in Hamburg.
Last season's runners-up Roma take on Feyenoord in the Italian capital after a 1-1 draw in the first leg.
Sporting Lisbon are 3-1 up on Swiss champions Young Boys going into the return fixture, while Galatasaray have a 3-2 edge over Sparta Prague.
The draw for the last 16 will be made at UEFA headquarters in Nyon on Friday.
