The veteran Croatia international struck twice as the German giants sealed a second-leg victory, booking their place in the last four of Europe's elite club competition
The German giants were in pole position to progress heading into the clash, having won the first leg 2-0 in France. And another 2-0 triumph in the return fixture saw them book their place in the last-four of Europe's elite club competition.
Ivica Olic, who two years ago scored a memorable hat-trick against Lyon, scored twice for Bayern before half-time, and his goals were all the hosts needed to advance.
The visitors made a bright start, and Loic Remy tested Manuel Neuer in the opening minutes after making a clever turn. Shortly thereafter, Benoit Cheyrou made an impressive run from deep and found Jeremy Morel, but the left-back's finish was kicked clear by the goalkeeper.
OM would rue their missed chances, as in the 13th minute, Olic opened the scoring. Franck Ribery made a mazy run into the right side of the box before crossing low, and the Croatian striker stabbed home from close range.
The visitors reacted well and continued their positive play, with Stephane Mbia's long-range blast forcing Neuer to tip over the bar. But Bayern gained full control of the match before the half-hour mark, as Toni Kroos and Anatoliy Tymoshchuk both forced fine saves from Steve Mandanda.
Thomas Muller, who before half-time was withdrawn due to an apparent hamstring injury, forced Mandanda into action on 30 minutes, with a glancing header, and Kroos shortly thereafter rattled the left post with another strong effort from outside the box.
Bayern kept up the pressure, and on 37 minutes, Olic completed his double on the counterattack. Ribery and David Alaba exchanged passes from deep in their own half before the Austrian crossed to Olic, who again finished from close range.
After the half-time break, the hosts stepped off the throttle as Marseille enjoyed more of the possession than before, but lacked incisiveness in the final third.
Ribery continued to be dangerous and forced a couple fine challenges to deny a look at goal before Kroos flashed another attempt narrowly wide.
As the final quarter of the match approached, Marseille had their best chance of the game, but Brandao's open header from inside the six-yard box missed over the bar.
The Brazilian striker's attempt would be an anomaly, however, as the final 20 minutes had a training ground feel about them. This suited Kroos, who was substituted without having been booked, as well as Jerome Boateng and Luiz Gustavo, who also avoided bookings that would have seen them slapped with a ban.
The result sees Bayern advance to the semi-finals, where they will face the winner of Real Madrid's tie with APOEL. Marseille will have to focus on Ligue 1 play from now to season's end.