Last updated on .From the section Champions League

Bayern Munich were unbeaten in both the league and Champions League before losing to Arsenal

Arsenal revived their Champions League hopes in thrilling fashion with a crucial victory over Bayern Munich at Emirates Stadium.

The Gunners' hopes of reaching the knockout phase were in serious jeopardy after they lost their opening two games away to Dinamo Zagreb and at home to Olympiakos.

Arsene Wenger's side responded by beating Pep Guardiola's Bayern - clear favourites to win Group F - and make a nonsense of those dismal earlier performances.

Bayern dominated possession but Arsenal dug out the win that keeps their hopes alive when substitute Olivier Giroud bundled home from close range in the 77th minute after goalkeeper Manuel Neuer made a rare error as he missed Santi Cazorla's free-kick.

Intense Arsenal display pleases Wenger

The win was secured in the dying seconds when Mesut Ozil turned in Hector Bellerin's cross, Neuer clawing the ball out only for the officials to adjudge it had crossed the line.

Arsenal were indebted to keeper Petr Cech, restored after replacement David Ospina's mistake in the defeat by Olympiakos, saving superbly from Thiago Alcantara and Arturo Vidal.

Neuer also excelled before his mistake, particularly with a sensational save from Theo Walcott's first-half header.

Relive how the Champions League action unfolded

Listen back to both Arsenal goals on BBC Radio 5 live

The different faces of Manuel Neuer

Neuer is widely regarded as the world's best - but it was a mixed night for Germany's World Cup winner.

He produced a save only the greats can contemplate when clawing out Walcott's close-range header when a goal seemed certain.

Could Walcott's header have been directed better? Did he give Neuer just that slight chance of making a save that the best will always take advantage of?

Yes, but it was still a monument to reflexes, agility and technique as Neuer left Walcott dumbfounded, as well as Aaron Ramsey, who had already turned to celebrate.

Neuer, however, proved he was fallible as Arsenal took the lead, making an ungainly dash from goal and flapping hopelessly at Cazorla's free-kick to allow Giroud to scramble home with a hint of handball.

It happens to the best - and it may just have saved Arsenal's Champions League campaign.

Manuel Neuer made four saves in the first half, the best a one-handed stop to deny Theo Walcott

Neuer's save was praised by a number of current and former footballers, with ex-Liverpool keeper Pepe Reina tweeting: "That's why he is the number one in the world."

Neuer had not conceded twice in one game this season before the trip to Arsenal

Cech proves a point

Arsenal manager Arsene Wenger was uncharacteristically touchy when it was suggested he made a mistake in preferring David Ospina to first choice Petr Cech in their previous Champions League game at home to Olympiakos.

It backfired as Ospina dropped a simple catch from a corner into his own net in the damaging 3-2 defeat.

Wenger was defiant in the face of claims he had made a serious error but the case against him only got stronger with 33-year-old Cech's return and performance against Bayern Munich.

Cech was in the action quickly with a superb reflex save from Thiago and also showed his enduring athleticism to save from Vidal.

This is not to suggest Ospina is a poor keeper - the Colombian is not - but when you have a keeper of Cech's quality at your disposal it is folly to leave him out of a game you cannot afford to lose.

Wenger did make a mistake when he dropped Cech. This game proved it.

Petr Cech was making his first appearance in the Champions League this season

The great Arsenal mystery

Arsenal's Champions League aspirations were wrecked last season by a performance of naivety and defensive incompetence in equal measure against Monaco in February when they lost 3-1 at home as they went out in the last 16.

The performance in defeat against Olympiakos was not far behind and left Arsenal fans infuriated.

Before that fixture, Wenger had said Arsenal "must win" all their home games but, after twice falling behind, they threw away the chance of a point when they conceded what proved the winner almost immediately after Alexis Sanchez's equaliser.

Arsenal (left) were camped inside their own half for much of the game, with only three players spending the majority in Bayern's half. In contrast, all but two of Bayern's outfield players (right) spent most of the game in Arsenal's half

How can a team that play so poorly against those opponents acquit themselves so well against Bayern Munich, accepted as a member of European football's royalty under the guidance of one of the game's great coaches in Pep Guardiola?

Guardiola is used to enjoying possession without victory at Emirates. When Barcelona lost a two-goal lead to draw here in April 2010, Arsenal only had 38% of possession - in the first half here Bayern enjoyed a 74.5% share.

And yet, once more, Arsenal dug in. They were defensively resilient, dogged in midfield and, even though the two goals were scrambled, they may well prove to be priceless.

Bayern Munich had a passing accuracy of 90.7% while Arsenal had 74.5%

Man of the match - Petr Cech

Wisely restored after being left out against Olympiakos. Authority, experience, excellence.

What this means for Arsenal

The Gunners remain bottom of the table, but are level on three points with Dinamo Zagreb and three behind both Olympiakos and Bayern Munich.

Wenger's side face Bayern at the Allianz Arena on 4 November, before hosting Dinamo later that month.

They finish their group stage campaign at Olympiakos on 9 December.

The top two in each group progress to the knockout stage, with the team finishing third going into the Europa League.

The pundit's view

John Hartson on BBC Radio 5 live: "This was a massive result. Arsenal needed a result and three points.

"They are firmly back in the group and it keeps the momentum going.

"They had to defend for their lives but what a win for Arsenal."

The stats you need to know

Olivier Giroud's past four goals for Arsenal have come from the bench

This is the first time Bayern have failed to win at Emirates Stadium, on their third visit

This was the first time Bayern failed to score in a Champions League group since December 2011, against Man City

Bayern Munich have won only one of their past six away games in the Champions League (D1 L4)

Arsene Wenger is the first manager to beat Pep Guardiola's Barcelona and Bayern Munich teams in the Champions League