By Toby Prince
The Gunners showed a different side to their play as they sat back and gave up possession for the majority of the game, while looking to hit on the break.
And their tactics worked perfectly as they took the lead through Giroud with 15 minutes remaining and wrapped up a deserved win when Ozil scored in injury time.
In the other group game, Nigeria striker, Brown Ideye, scored a late winner to hand Olympiakos a 1-0 victory over Dinamo Zagreb in Croatia.
The 27-year-old got the most of a cross from Dimitris Siovas, racing down the left with no support before surging past two defenders and goalkeeper Eduardo to score in the 79th minute.
It secured a second consecutive away win for the Greek champions in Group F after beating Arsenal last time.
The results mean Arsene Wenger’s men are now third on three points after three games, three behind Bayern and Olympiakos in first and second places respectively.
Eden Hazard and Willian hit the woodwork as Chelsea were held to a goalless draw at Dynamo Kiev.
It was a vastly improved display, but the Blues stayed third in Group G behind FC Porto and Dynamo, who remained unbeaten.
Chelsea coach, Jose Mourinho, was critical of the referee’s officiating describing him as “weak and naïve” after the match.
Mourinho faulted the ref’s decision not to award his side a penalty in the first half when Cesc Fabregas was brought down by Serhiy Rybalka.
Full Tuesday results
Arsenal 2-0 Bayern Munich
Dynamo Kiev 0-0 Chelsea
FC Porto 2-0 Maccabi Tel Aviv
Dynamo Zagreb 0-1 Olympiakos
Valencia 2-1 Gent
Bate 0-2 Barcelona
Bayern Leverkusen 4-4 Roma
Zenit St. Petersburg 3-1 Lyon