There were chances galore for both sides but it was not until the 63rd minute that Jack Wilshere blasted Arsenal ahead with a superb finish past Thibaut Courtois.
Bellerin tripped Hazard four minutes later and Hazard tucked away the penalty and Chelsea appeared to be heading back into second spot when Marcos Alonso struck from close range.
Bellerin made sure Arsenal earned the point they deserved, however, with a sublime half-volley in the second minute of stoppage time.
There was still time for Chelsea substitute Davide Zappacosta to hit the crossbar but a draw was a fair result. Chelsea remained in third place with 46 points, 16 behind leaders Manchester City, and Arsenal stayed sixth.