Fraser earned them a replay a minute after coming on following a three-goal burst by Pools in the space of 16 minutes after the break.
Hartlepool won a dour encounter 1-0 in the north east when the teams met in League One a fortnight ago. This FA Cup clash was much more eventful at a wet and windy Withdean.
Hartlepool were the better team in the first half and yet found themselves trailing at the break.
Brighton went ahead in the 19th minute when a crossfield pass from Dean Cox found Stuart Fleetwood, looking suspiciously offside.
He set up Kevin McLeod, who caught keeper Arran Lee-Barrett off his line with a perfectly executed chip.
Brighton doubled their advantage in the 38th minute. Fleetwood exchanged passes with Adam Virgo before finding Cox and he drove in his second goal in three games.
Hartlepool boss Danny Wilson made a double substitution at the break, bringing on David Foley and Matty Robson, with James Brown pushed up front alongside Joel Porter.
The move soon paid off as Brown's cross to the near post was headed into his own net by the diving Colin Hawkins.
The visitors were level two minutes later. Ritchie Jones made a strong run through midfield and, when the Brighton defence failed to deal with Andy Monkhouse's cross, Brown had time to turn and score from eight yards.
Hartlepool's remarkable comeback appeared complete in the 69th minute when the Brighton defence failed to clear a corner. Monkhouse exchanged passes with Clark before rifling in a right-foot finish.
Brighton chief Micky Adams also made a double substitution 13 minutes from time, introducing Fraser and Jake Robinson.
It paid off immediately as Robinson was involved in a chaotic sequence inside the Hartlepool area. An angled drive from Fleetwood was hacked off the line, but Fraser drove the loose ball into the roof of the net.
The replay takes place at Victoria Park on November 18.