Eden Hazard's penalty cancelled out Jack Wilshere's opener before Marcos Alonso looked to have sealed the turnaround for the champion, only for Bellerin to blast home at the death.
The result means Antonio Conte's side stays third in the table, a point behind Manchester United and 16 adrift of runaway leader Manchester City, having won just once in its last five away league matches.
It was Wilshere who broke the deadlock in the 63rd minute with an emphatic finish but Arsenal's lead lasted only four minutes, with Hazard winning and then converting a debatable spot-kick after Bellerin sent him to ground in the box.
Alonso snatched what he thought was the winner six minutes from time, but Arsenal showed great resolve to push for an equaliser and Bellerin atoned in the 92nd minute with a stunning half-volley from the edge of the area.
Chelsea still had another chance to claim all three points, but Alvaro Morata's wasteful finishing reared it's head again and substitute Davide Zappacosta hit the crossbar with his follow-up.
The result will likely cause more frustration for Arsene Wenger, who was hit with an FA charge after complaining about the penalty awarded to West Brom in last Monday's 1-1 draw at The Hawthorns, though, as it means his side stay sixth in the table, five points adrift of the top four.