The visitors had even started the second half the brighter of the two sides but lost captain Koscielny to a muscle injury just as they looked at their most risky.
The visitors then had a golden opportunity to pull ahead just before half time when Ozil was through on Neuer, but sent his shot straight at the custodian.
Thiago Alcantara struck twice and Arjen Robben, Robert Lewandowski and substitute Thomas Mueller were also on target as the Bavarians inflicted Arsenal's first defeat of the season in Europe's premier club competition.
Arsenal recovered from conceding an early goal to equalise and the game was poised at 1-1 at halftime before the Premier League club's key defender Laurent Koscielny was forced off through injury early in the second half.More news: Eight killed in Kashmir gunfight, protestors clash with security
"The real problems were after the third goal". The midfielder was equally composed in front of goal and made no mistake with his finish. "Before that, we controlled them quite well".
Arsenal were eventually breached for a fourth time on 64 minutes when Thiago's effort from the edge of the box deflected off Xhaka, sending the ball spinning past a helpless Ospina.
But there was nothing the Colombian could do about Muller's goal, as he finished calmly after being introduced as a late replacement.
Robben said Bayern had proved their recovery from a recent dip in form.More news: Flower shops brace for Valentine's Day
The only previous Champions League encounter between Carlo Ancelotti and Arsene Wenger was in the 2007/08 Champions League round of 16. Perhaps with this in mind Arsène Wenger was particularly brusque with the suggestion that his team's ability to break a six-season run of instant elimination from the Champions League knockout stages might be a decisive factor in his own continued tenure as Arsenal coach.
Mesut Ozil at Emirates Stadium, London, February 11.
Meanwhile, Wenger offered no excuses for his team's second-half collapse.
"It is hard to explain", the Arsenal boss told BT Sport. It's very hard just after a game [to analyse], it's a shock as well to lose at that level and on top of that we made everything wrong - the fifth goal shows that. We have an advantage to play the second game at home.More news: Google uses Valentine's Day doodle to bring awareness to endangered animal
"Arsenal had the opportunity to equalise after we had a good opportunity to score a second goal".