An early Robert Lewandowski penalty looked to have won the match for the Bavarian giants, but Alex Iwobi headed home from an Aaron Ramsey cross in added time to earn the Gunners a 1-1 draw in normal time.
Bayern, who came out on top 10-2 when these sides met over two legs in the last 16 of the Champions League earlier this year, dominated for large parts of the match but were ultimately punished after failing to put their opponents away.
It was Bayern who looked the sharper throughout the opening 45 minutes, though, netting nine minutes in from the spot after Bernat was clumsily challenged by makeshift wing-back Ainsley Maitland-Niles, allowing Lewandowski to tuck away.
The Bavarian club included recently-retired goalkeeper Tom Starke in their starting lineup due to a couple of injury issues, and he was needed twice in the first half to keep out a close-range volley from Mesut Ozil and a one-on-one from Alexandre Lacazette.
Record signing Lacazette looked favourite to score his second goal of pre-season when latching on to Ozil's through-ball, only for the veteran stopper to produce a big save down low.
The offside flag was wrongly raised on that occasion, while Cech proved the hero later in the half to deny Thomas Muller, Benat and James Rodriguez in the space of five minutes.
It was no surprise to see Arsenal's three-man backline being given its sternest test yet, with boss Arsene Wenger forced into a change before the half was out by bringing on Reiss Nelson for a seemingly unwell Sead Kolasinac.
Arsenal altered their formation for the second half but the flow of the match remained the same - Bayern bossing things in terms of chances, as half-time replacement Kingsley Coman spotted two men over in the middle.
Lewandowski surprisingly turned down the invitation to shoot from a few yards out, instead leaving it for Rodriguez who saw his attempt from 10 yards out pushed aside by Cech at his near post.
Alaba was the next to test Cech, this time from a free kick that dipped over the wall and towards the bottom corner of the net, if not for the Czech's intervention.
The intensity levels dropped considerably in the final half-hour of the match in the humid Shanghai heat, however, with the sides struggling to create clear-cut openings.
Replacement keeper Christian Fruchtl was called into action for the first time late on to catch Theo Walcott's curled shot, but Arsenal did manage to level in the third minute of added time when Iwobi converted Ramsey's cross, before using the momentum to prevail on pens.