An uncharacteristic error from Manuel Neuer helped Arsenal reignite their Champions League hopes with a 2-0 win over Bayern Munich.
Arsene Wenger's side headed into the Emirates Stadium contest with their Group F campaign in disarray following losses to Dinamo Zagreb and Olympiacos.
But they 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 their customary mastery of possession served to make the second half one for Arsenal to endure rather than enjoy.
But stunningly, 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 Bavarians' first defeat after 12 consecutive wins in all competitions was confirmed by a breakaway Ozil goal in stoppage time.
Arsenal remain three points shy of the qualification places following Olympiacos' victory by the same scoreline in Zagreb but taking the spoils from the Bundesliga giants who have ended their past two 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 were 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 Germany international 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 following 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 they were grateful to see Sanchez blaze over following 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.
And it was a far less esteemed goalkeeping effort from Cazorla's set-piece a few moments later that allowed Giroud to celebrate joyously.
As Bayern pressed for the share of the spoils they deserved, Arsenal broke clinically. 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.