An uncharacteristic error from Manuel Neuer helped Arsenal reignite its UEFA Champions League hopes with a 2-0 win over Bayern Munich at the Emirates Stadium.

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Arsene Wenger's side headed into the contest with its Group F campaign in disarray after defeats to Dinamo Zagreb and Olympiacos.

But the hosts played a full part in a thrilling opening half, with Neuer forced into brilliant saves from Mesut Ozil and Theo Walcott – the latter from the England man a truly astonishing piece of goalkeeping.

Bayern also threatened, particularly through the effervescent Douglas Costa, and its customary mastery of possession served to make the second half one for Arsenal to endure rather than enjoy.

But somehow, Neuer undid his earlier heroics by woefully misreading Santi Cazorla's hopeful punt into the box for Giroud – introduced three minutes previously in place of Walcott – to smuggle home a 77th-minute header.

The Bavarian side's first defeat after 12 consecutive wins in all competitions was confirmed by a breakaway Ozil goal in stoppage time, which needed the goalline official to award it to the Gunners and seal a famous win.

Arsenal remains three points shy of the qualification places after Olympiacos's victory by the same scoreline in Zagreb, but taking the spoils from the Bundesliga giant, which has ended the past two Arsenal Champions League campaigns, leaves Wenger's men firmly in contention this time around.

Full-back Hector Bellerin made an important challenge to deny in-form striker Robert Lewandowski inside the first minute but Arsenal was soon showing the "animal" intensity that Bayern coach Pep Guardiola anticipated during his pre-match media conference.

A section of Bayern fans, who boycotted the first five minutes in protest against Arsenal's ticket prices, were welcomed by applause from the home support – and their team almost falling behind.

Alexis Sanchez burst infield to feed Ozil, who drew a sharp stop from his Germany team-mate Neuer before Philipp Lahm blocked Walcott's follow-up.

Neuer's opposite number Petr Cech – controversially rested for Arsenal's opening Champions League defeats – denied Thiago Alcantara after a slick one-two between the Spaniard and Thomas Muller.

Cech also thwarted Costa from a tight angle after the Bayern winger perplexed Bellerin with some audacious footwork.

Bayern appeared to be in control when Cech kept out an Arturo Vidal drive, although it was grateful to see Sanchez blaze over after a partially cleared 31st-minute corner.

Further Arsenal encouragement came as Neuer saved stupendously from Walcott and Aaron Ramsey's shot on the rebound was scrambled clear.

The increased confidence displayed by Wenger's men almost cost them as half-time approached, Sanchez carelessly coughing up possession for Costa to charge into the box and shoot over.

Costa continued to threaten after the restart, sending a rasping left-footed effort just beyond the top corner, while Lewandowski forced Cech to tip over a sweetly struck shot from the edge of the box.

The exertions of chasing Bayern's relentless manipulation of possession took a particular toll on Ramsey, who departed in the 57th minute with a hamstring strain.

Cech underlined his worth once more, prevailing where many keepers have failed of late in a one-on-one against Lewandowski in the 75th minute.

"He kept us in the game," Wenger admitted after the game. "But the saves of Neuer too, they kept them in the game as well. You have two world class goalkeepers out there tonight.

But it was a far less esteemed goalkeeping effort from Cazorla's set-piece a few moments later that allowed Giroud to celebrate Arsenal's opener.

As Bayern pressed for a share of the spoils, Arsenal broke clinically to create its second. Neuer thought he had denied Ozil from Bellerin's cross, but the additional official behind the goal correctly ruled otherwise to crown a famous victory for the Premier League side.

"Until now, I think we were are only focused on the Premier League," said Wenger. "We neglected (the Champions League), perhaps subconsciously, for the defeats against Kiev and Olympiacos. I hope this win will convince my players we can now play a part in the Champions League as well."