Also on Thursday, Freiburg advanced after coming back from a 2-0 deficit to claim a 3-2 win against Lens in extra-time.
Michael Gregoritsch scored the winner in the 99th minute, but only after Roland Sallai completed a dramatic brace to settle the 2-2 draw in the final minutes of regular time.
Milan, who won 3-0 at the San Siro last week, eliminated their French opponents with a 5-3 aggregate score.
The Italian powerhouse, seven-time European champions, have never won the second-tier Europa League or its predecessor, the UEFA Cup.
Midfielder Benjamin Bourigeaud's hat-trick put the hosts up three times with Milan quickly answering twice.
Bourigeaud netted the opener in the 11th minute with a fierce right-footed shot from over 20 metres to beat goalkeeper Mike Maignan.
Forward Luka Jović cancelled it out 10 minutes later with a header off a cross by captain Theo Hernández.
Bourigeaud made it 2-1 early in the second from the penalty spot but Rafael Leão equalised after four minutes on a fine solo effort.
Bourigeaud sent Maignan the wrong way with another spot kick to make it 3-2.
Marseille's new coach Jean-Louis Gasset made a victorious debut after he was appointed Tuesday to replace Gennaro Gattuso.
Geoffrey Kondogbia and substitute Ismaïla Sarr sealed a 3-1 win for Marseille over Shakhtar Donetsk with a goal each in the second half. Marseille advanced 5-3 on aggregate.
Earlier, Marseille striker Pierre-Emerick Aubameyang netted his 31st career goal in the Europa League to break the competition record and level the tie after Georgiy Sudakov converted from the spot.
Sporting were held 1-1 at home by Young Boys but advanced 4-2 overall.
Two-time European champions Benfica held hosts Toulouse 0-0 to progress 2-1 on aggregate, while Qarabag lost 3-2 to Braga at home but progressed 6-5 on aggregate.
Roma beat Feyenoord 4-2 on penalties after the teams drew 1-1 in the second leg and were locked at 2-2 in the tie.
The eight runners-up in the Europa League group stage played the eight third-place teams from the Champions League group stage in the playoffs.
The eight winners will take on the Europa League's group winners, who qualified directly for the round of 16. They are Liverpool, West Ham and Brighton from the Premier League, as well Leverkusen, Atalanta, Villarreal, Rangers and Slavia Prague.
The draw is scheduled for Friday.
In the third-tier Conference, Dinamo Zagreb drew 1-1 and secured a spot in the next round at the expense of Real Betis while Servette's lone goal at Ludogorets was enough to advance after a 0-0 draw in the first leg.
Ajax beat Bodo/Glimt away 2-1 to progress 4-3 on aggregate, while Olympiacos advanced 2-0 with a 1-0 win over Ferencvaros.
Molde, Sturm Graz and Union Saint-Gilloise also progressed.
The competition's playoffs features the runner-up teams from the group stage facing the third-place finishers in the Europa League group stage. The eight group winners, including Aston Villa and last year's runner-up Fiorentina, have advanced to the last 16.
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