Bayern extended their Champions League record to 16 home wins by flooring the Gunners with three goals in ten second-half minutes.
Bayern knocked Arsenal out at the same stage in 2005, 2013 and 2014 and were looking comfortably placed to make it four times after romping through Wednesday's first leg.
The Allianz Arena defeat raises the pressure on Wenger for the return leg on March 7 with only Alexis Sanchez's away goal for comfort.
Arjen Robben's superb curling shot gave Bayern the lead on 11 minutes, but Sanchez levelled by drilling home Manuel Neuer's save from a penalty on 30 minutes.
Bayern moved up a gear after the break with a flurry of goals in quick succession. Robert Lewandowski headed Bayern back into the lead on 53 minutes before Thiago added two in quick succession while Thomas Mueller came off the bench to complete the rout.
Bayern spent the opening minutes camped in the Arsenal half and took the lead on 10 minutes through Robben's wonderful strike. The Dutch winger cut in from the right, and curled home a superbly-weighted shot off his left foot from outside the area.
Mesut Ozil drilled the resulting free-kick at Neuer, but moments later Arsenal were awarded a penalty. Lewandowski mistimed his clearance kick in the area and struck Laurent Koscielny's raised leg.
Despite Bayern's furious protests, Serbian referee Milorad Mazic pointed to the spot. Neuer saved Sanchez's penalty, but the Chile international drilled home the rebound from a tight angle at the second attempt.
It was the valuable away goal Bayern had talked about not conceding in the match's build-up.
It was 1-1 at the break, but Bayern stepped up the pressure in the second half. Robben released Philipp Lahm who put in a perfect cross and Lewandowski twisted to tuck his header past David Ospina's reach.
The Poland hot-shot then flicked Xabi Alonso's pass into Thiago's path to tuck his shot past Ospina.
Lewandowski hit the crossbar on 61 minutes, but Thiago added his second when his shot from the edge of the box deflected past the Arsenal goalkeeper on 63 minutes.
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