The Germans had arrived at the Emirates Stadium in imperious form following a new Bundesliga record of nine consecutive victories, while they topped Group F with maximum points from their two European ties
However, Arsenal - who were bottom of the table following successive defeats - produced a resolute display and took the lead with 13 minutes left when substitute Olivier Giroud headed in after a mistake from goalkeeper Manuel Neuer, who had earlier produced a brilliant save to deny Theo Walcott
German playmaker Mesut Ozil scored a second in stoppage time to seal the win, his close-range effort given by the fifth official after Neuer had clawed the ball back from over the goalline
While the Gunners still have it all to do to qualify for the knockout stages following Olympiacos' win away to Dinamo Zagreb, and next travel to Munich in November, Wenger has no doubt his Barclays Premier League high-flyers are starting to deliver the consistency required to challenge the very best
"It can strengthen our belief and strengthen the belief of people of around us, our fans," said the Gunners boss, who lost midfielder Aaron Ramsey to a hamstring injury in the second half
"We won 3-0 against Manchester United, 3-0 against Watford and 2-0 (over Bayern), so it is important we have a good balance between defending well and attacking well
As long as we defend well and score goals then the balance is right."
Arsenal are now third in Group F, but still need other results to go their way to be certain of reaching the knockout stages.
"We had an absolute necessity to win the game and we did it in an intense and disciplined way,'' said Wenger
''It was a top-level game between two top-level teams
Bayern had more possession than us, but we decided to make it tight in our final third and catch them on the break
"Overall we have beaten a very strong team and kept a good level focus from the first to the last minute and kept a clean sheet as well.''
Wenger added: ''We (still) need a result at Bayern
Now let's focus on Everton (in the Premier League on Saturday).''
Pep Guardiola, who had not seen his Bayern side lose inside 90 minutes this season, refused to blame Neuer's flap for costing Bayern a result in London and was pleased with what his injury-hit team produced
''Never in my life have I criticised a player for taking decisions if correct or not correct
We did not lose because of Manuel Neuer
This is football and he took a decision in that situation - that is it," Guardiola said
''I'm so proud of my team
I like to win so I'm not happy but we played with a lot of courage to come here and take the ball off of the Arsenal players."
Source : PA
Source: PA