Kevin McLeod gave the Seagulls the lead in the 19th minute against the run of play with a delightful chip from the edge of the box.
And dominant Hartlepool found themselves further behind in the 38th minute when Dean Cox, played in by Stuart Fleetwood, shot low into the corner past goalkeeper Arran Lee-Barrett.
But Pools were back in the match thanks to a 53rd-minute own goal from defender Colin Hawkins, who headed in a James Brown cross at the near post.
The lively Brown cashed in on defensive hesitancy to swivel and shoot into the bottom corner two minutes later, before Andy Monkhouse gave the visitors the lead when Brighton failed to clear a corner after 69 minutes.
But midfielder Fraser struck within two minutes of his introduction to save Brighton 12 minutes from time after McLeod's shot was cleared off the line.