Marcos Alonso’s 84th-minute strike looked to have secured a vital three points for the champions, but Bellerin struck deep into stoppage-time as the points were shared.
Jack Wilshere’s first Premier League goal since May 2015 had fired the Gunners into a deserved 63rd-minute lead, but Eden Hazard hauled Chelsea level from the penalty spot four minutes later.
The result sees Chelsea and Arsenal remain third and sixth in the Premier League, with both teams missing the chance to leapfrog Manchester United and Tottenham respectively.
Alexis Sanchez and Mesut Ozil were chief tormentors to the Chelsea defence in a pulsating first half, but the game’s first chance fell to Alvaro Morata, who fired woefully wide on 14 minutes after misjudgement from Calum Chambers released him on goal.
The game then burst into life on 17 minutes. Seconds after an Ainsley-Maitland Niles penalty appeal was declined, Thibaut Courtois tipped a fierce Sanchez drive onto both posts before smothering the rebound.
The Belgium international was in inspired form, denying Alexandre Lacazette’s low effort at full stretch. His counterpart Petr Cech, meanwhile, had to be alert to tip Tiemoue Bakayoko’s rasping effort over on 28 minutes.
Ozil flashed a shot inches wide on 39 minutes before Cesc Fabregas’ curling effort drifted wide on the stroke of half-time, after which Cech was on hand to deny Hazard’s low effort and Alonso’s header in quick succession.
Arsenal soon regained the initiative, though, with Lacazette drawing another save from Courtois before his resolve was finally broken by Wilshere’s thunderous near-post drive on 63 minutes.
However, the Gunners’ lead lasted just four minutes as Bellerin was penalised for a foul in the area on Hazard, and the Belgian dusted himself down to haul Chelsea level from the spot.
Morata fired over on 71 minutes and a deflected N’Golo Kante shot narrowly missed the target as the champions pushed for a second, which came when Alonso poked Davide Zappacosta’s cross home from close range.
Back came Arsenal in a thrilling finale as Bellerin’s whipped effort flashed past Courtois in stoppage-time, but the Gunners almost lost it again as Cech thwarted Morata before Zappacosta thundered the rebound against the crossbar in the dying seconds.