Arsenal's night began to do downhill from the seventh minute when Ozil earned a penalty after being felled by Jerome Boateng only to miss the spot-kick as his weak effort down the middle was clawed clear by the right hand of Manuel Neuer.
It went from bad to worse when Szczesny was red carded after he sent Robben crashing to the ground as the Dutch winger burst in on goal on 36 minutes. Arsenal were handed a reprieve when David Alaba hit the post with substitute goalkeeper Lukasz Fabianski heading in the opposite direction.
But the loss of a man proved too much of a hurdle for Arsene Wenger's side to overcome as Philipp Lahm found Toni Kroos, who left Fabianski with no chance from distance for the opening goal on 54 minutes.
With Robben stretching the home side as much as possible, Arsenal were forced to defend stoutly, only to be undone again when substitute Thomas Mueller arrived to head into the net from a Lahm cross with two minutes remaining.
Arsenal won 2-0 in Munich at the same stage of this tournament a year ago, but will need to replicate that outcome to force extra-time against the Champions League holders in the second leg on March 11. It looks highly likely that Arsenal will depart at the last-16 stage.
4' - SZCZESNY SAVE: Kroos unloads a shot from 25 yards out, and a brilliant diving stop by Wojciech Szczesny to nudge the ball wide. So close to an opening goal for Bayern. That was a terrific stop.
7' - ARSENAL EARN PENALTY: Ozil taken out late by Boateng, who is booked for that tackle. Was a soft penalty, but was a penalty.
8' - NEUER WITH THE SAVE: Ozil goes down the middle. Neuer stays up long enough before swatting the kick away with his right hand. Poor penalty.
36' - PENALTY TO BAYERN AND A RED CARD! Wojciech Szczesny has been sent off as he clips Robben in the air. Monreal failed to pick up the run of Robben. Poor defending by Monreal.
37' - ALABA MISSED THE PENALTY: Alaba misses the penalty. Ball comes off a post as Fabianski dived to his left. Two penalties have been missed. Score remains at 0-0. But Arsenal are one man down.
53' - FABIANSKI WITH THE SAVE: Robben works the angle well. Cuts inside before nudging a shot at the goal from 18 yards. Decent stop by Fabianski low to his right.
54' - KROOS FINDS THE OPENER: Kroos slams the ball high into the net from the Lahm pass. Gorgeous strike from distance. And that is a 1-0 lead for the visiting side.
69' - ROBBEN SEES A SHOT SPIN INCHES WIDE: Robben decides to try his luck, but the shot spins a few yards wide of goal. Brilliant effort. Almost a superb goal from the Dutchman.
88' - MULLER ADDS THE SECOND: Mueller heads into the gaping net from the Lahm cross. And that is that. A 2-0 lead for Bayern. Should be all over now.
90+1' - KROOS HITS A POST: Kroos slams a shot from distance against a post. So close to that third goal. Brilliant really from Bayern against 10 men.
Arsenal managed just 12% possession in the second half versus Bayern Munich, completing just 38 passes after half-time.
Philipp Lahm has assisted Bayern Munich's last 3 goals against Arsenal in the Champions League.
Toni Kroos' goal was the 100th that Bayern have scored in all competitions this season.
The 100 red cards for Arsenal under Arsene Wenger have been given to 50 different players & against 42 different opponents.
Arjen Robben has won 3 penalties in the Champions League this season, more than any other player.
TALKING POINT: What can Arsenal take out of the night? This was a chastening evening for the home side and their fans, but Wenger can be happy with the application of his 10 men despite being given a serious run-around. It is doubtful if the home side would have avoided defeat with 11 men as Bayern are on a different level from Arsenal. There was a reason why Arsenal went down to 10 men, Bayern's movement caused the sending off such is the game of football. Pep Guardiola's side have so much more to offer this tournament than Wenger's team.
MAN OF THE MATCH
Arjen Robben (Bayern Munich) - Such a terrific player, Robben is one of the world's most intelligent attackers. Earned the penalty and treated the 3,000 visiting fans to a professional masterclass in how to play against 10 men in the second half by stretching the home side all over the park.
Arsenal: Szczesny 7, Sagna 6, Mertesacker 7, Koscielny 7, Gibbs 5, Flamini 6, Wilshere 5, Oxlade-Chamberlain 6, Ozil 3, Cazorla 4, Sanogo 6. Subs: Fabianski 7, Monreal 5, Rosicky 6
Bayern Munich: Neuer 8; Lahm 8, Boateng 5, Dante 6, Alaba 6; Martinez 7; Robben 8, Kroos 8, Thiago 6, Gotze 7; Mandzukic 6. Subs: Rafinha 6, Pizarro 6, Mueller 7
THE MATCH IN A TWEET