From beginning to end at the Emirates Stadium, both sides traded chances with Arsenal keeper Petr Cech and his opposite number Thibaut Courtois responsible for keeping the scoresheet blank until past the hour mark.
Jack Wilshere gave Arsenal a 63rd-minute lead but Bellerin's trip on Eden Hazard gave the Belgian wizard the chance to level from the penalty spot four minutes later.
Wilshere shows he is no mere Jack of all trades
A flowing Chelsea move ended with Marcos Alonso putting the visitors ahead in the 84th minute but they were denied the victory that would have put them above Manchester United into second spot with Bellerin's sumptuous 92nd minute half-volley.
There was still time for Chelsea substitute Davide Zappacosta to hit the crossbar but defeat would have been harsh on Arsenal who had 14 goal attempts to Chelsea's 19.
Chelsea remained in third place with 46 points, 16 behind leaders Manchester City, who have a 15-point lead over second-placed Manchester United, while Arsenal stayed sixth.
Arsenal's Giroud out of Liverpool clash
It was manager Arsene Wenger's 60th match against Chelsea in his long Arsenal reign but few could have provided as much goalmouth action as this classic.
"It was a fantastic football game and overall it could have gone both ways," said Wenger. "Maybe it's a fair result. The penalty was a farcical decision. When we looked as though maybe mentally we were shot, we had the resources to come back to 2-2."
Alvaro Morata, strangely profligate all night, wasted a great chance early on for Chelsea when he took advantage of a yawning chasm in the Arsenal defence to go through on goal but his sidefoot finish was dreadful.
At the other end Alexis Sanchez's shot struck both uprights after a superb save by Courtois who shortly afterwards did brilliantly to keep out Alexandre Lacazette's shot.
Tiemoue Bakayoko and Cesc Fabregas both wasted chances for Chelsea while Mesut Ozil drew a fine save from Courtois. Former Chelsea stopper Cech, seeking a 200th Premier League clean sheet, showed his class to deny Hazard as the second half began with another flurry of attacks.
Not to be outdone, Courtois then blocked Sanchez's powerful close-range effort after the Chilean's sublime piece of trickery.
Wilshere finally beat Courtois, the midfielder lashing a left-foot shot high into the top corner on the stretch after a deflected pass found him at the far post.
Arsenal were buoyant but were flattened four minutes later when Bellerin dangled a leg and Hazard went down theatrically — much to the annoyance of Wenger, whose side were denied victory at West Bromwich Albion by a late penalty on Sunday.
Hazard sent Cech the wrong way from the spot. A sweeping crossfield move in the 84th minute saw Zappacosta get the better of Arsenal's inexperienced left back Ainsley Maitland-Niles before rifling in a low cross that Alonso met sweetly to give Cech no chance.
To their credit Arsenal refused to accept defeat and when Alonso failed to get proper distance on a clearing header the ball feel for Bellerin to send a half-volley curling away from the helpless Courtois.
Morata spurned another one-on-one before Zappacosta's dipper cannoned against the crossbar to leave honours even to the frustration of Chelsea manager Antonio Conte.
"I think it is a pity because when you have so many chances to score you must win the game," said Conte.
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