CNN  — 

The time of possession between Arsenal and Bayern Munich was lopsided, but matches are won on the scoreboard.

Arsenal super-sub Olivier Giroud delivered the first goal of the match in the 77th minute – just 3 minutes after replacing Theo Walcott – on a night of exemplary goalkeeping up to that point.

German international Mesut Ozil knocked in a second goal for the Gunners in the 93rd minute, sealing a 2-0 result and one of the biggest Champions League wins for the club in recent memory.

In a match where Arsenal reversed its normal attacking strategy by giving up possession to Bayern Munich in return for breakaway chances, a goalless draw – and a likely end to Arsenal’s European dreams –appeared to be in the cards until late.

But Giroud’s crawling header that came under a clatter of confusion from a dangerous Santi Carzola free kick changed everything. Though the ball appeared to brush off Giroud’s nose on the way to the goal, it was unclear whether it also touched any part of his arms.

“This goal relieved us,” said the Frenchman moments after the match. “We did well until this goal, and we defended really well. We knew that Bayern Munich will have the ball because they are doing very well in possession.”

Indeed, Bayern dominated the ball with a nearly unheard-of 73% possession rate at the Emirates, though that appeared to be by design.

“Yes they dominated the game, but we knew that (they could). But we had passion, and finally we succeeded to score and we finished the job with Mesut Ozil,” Giroud added. “We needed this win to stay in the Champions League run, to qualify for the next stage, we knew that it would be difficult but we have done it.”

Giroud – who for the moment has lost his lone striker role to Theo Walcott – was also quick to acknowledge Arsenal’s goalkeeper for the eight crucial saves he made.

“We have to thank as well Petr (Cech) because he (had) a fantastic game. We are all pleased tonight, because we played against a fantastic team. That’s nice for the future and for the following games. We need to keep the confidence high,” he said.

Before the late blunder where he appeared to have lost sight of the ball, Manuel Neuer showed why he’s considered by many to be the world’s best goalie. A stunning save of Theo Walcott’s close range header at the 32nd minute was met with gasps from Walcott and the home crowd. Walcott was a constant threat to Bayern, yet was never able to finish.

Not to be completely outdone, Arsenal’s Petr Cech made several key saves of his own from Douglas Costa in the 18th minute and Arturo Vidal in the 27th minute. A breakaway moment from red-hot Robert Lewandowski was stifled by Cech in the 74th minute.

“We had an absolute necessity to win the game and we did it in an intense disciplined way. It was a top level game between two disciplined teams,” said Arsenal manager Arsene Wenger after the match.

“Bayern had more possession than us but we decided to make it tight in our final third and catch them on the break. Overall I think we have beaten a very strong team and we kept a good level of focus from the first to the last minute, and we kept a clean sheet as well,” he added.

Bayern’s manager Pep Guardiola – who suffered a pre-match distraction when his team bus was involved in a minor road accident in London – was generous in his praise to the home side.

“Obviously Arsenal have very, very good players, fast players. But ..we showed we are able to compete, to come here with personality and play,” he said. “After that, I can just say congratulations for Arsenal.”

Bayern’s away fans staged a boycott of the match for the first five minutes to express their displeasure in what they felt was high ticket prices levied on them by the hosts, at an average of £64 ($99). They held up signs that read “£64 a ticket but without fans football is not worth a penny.”

Bayern have won all nine of their league matches so far, scoring 29 while conceding only four goals. They also won their first two Champions League matches by a combined score of 8-0.

Arsenal midfielder Aaron Ramsey came off with an injured hamstring in the 56th minute, and was replaced by Alex Oxlade-Chamberlain.

After losing to Olympiacos and Dinamo Zagreb, Arsenal finally picked up their first points in the group. They moved up to third place with three matches to be played, including an away rematch with Bayern on November 4.

In other action, Olympiacos beat Dinamo Zagreb 1-0, while Chelsea drew 0-0 away at Dynamo Kyiv. Barcelona beat FC BATE Borisov 2-0 away, while Roma and Bayer drew 4-4.