The Bavarians were held to a 1-1 draw by the Gunners at the Allianz Arena tonight but their 2-0 victory in north London last month was enough to see them through to the final eight.
Arsene Wenger's Arsenal side were slow to start in Bavaria and found themselves a goal down on the night when Bastian Schweinsteiger, who lost Santi Cazorla, was allowed to waltz into the area to finish Franck Ribery's pass from close range in the 55th minute.
The Gunners hit back immediately through former Munich striker Lukas Podolski who dispossessed captain Philipp Lahm near the byline before advancing towards Manuel Neuer and unleashing a fierce angled effort which rippled the back of the net.
The first half was completely controlled by Bayern with Arsenal providing little in the way of goalscoring chances while Pep Guardiola's men did as they pleased, skipping forward with what appeared to be consummate ease.
However, the visitors altered their mindset - particularly after Bayern's opening goal - and looked to get on the front foot in order to bridge the two-goal deficit.
Bayern's stingy defence were at it again though and continued to deny Arsenal the opportunity of winning any easy balls and producing counter-attacking movement.
As Arsenal tired, Bayern went on the attack and won a penalty in injury-time when Arjen Robben again threw himself to the floor theatrically although this time, there was actually some sort of contact from Laurent Koscielny.
Substitute Thomas Muller stepped up to the spot in the hope of sending the Gunners packing but Lukasz Fabianski, deputising for the suspended Wojciech Szczesny, denied the German international with his legs before scampering to send the ball away from the goal-line as it spun gilt-edged on the chalk.
In the end, however, last season's Champions League, Bundesliga and DFB-Pokal acquirers deserved to move through to the quarter-finals as they put their name in the hat for a sixth title in Europe's premier club competition.
The draw for the Champions League quarter-finals will be held on March 21 when all the Round of 16 second legs have been completed. The first legs of the quarters will be played on April 1 and 2, and the second legs will be played on April 8 and 9.
2013/14 UEFA Champions League - Round of 16 second leg
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