Yannick Sagbo struck a late equaliser for the Barclays Premier League side.
The Seagulls looked set to reach the last-eight juncture for the first time since 1986 thanks to Leonardo Ulloa's quality first-half goal, only to see a mouth-watering home clash with Sunderland and former manager Gus Poyet put on hold.
The Uruguayan's three-and-a-half year spell with the Seagulls came to acrimonious end in the summer, with his first return to the Amex Stadium dependent on whether Brighton can win the replay after Sagbo's late strike made it 1-1.
It led to a frantic end to what had been for the most part a disjointed match, thanks in no small part to the sides' combined 13 changes for the fifth-round clash.
There were few chances of note until Sagbo stretched to send an unconventional volley onto the crossbar in the 27th minute - a strike that appeared to kick-start proceedings.
Just three minutes later Brighton went ahead through Ulloa, who played an impressive one-two with Will Buckley before dinking over Allan McGregor.
Hull threatened an immediate leveller as Curtis Davies' header hit the woodwork, but that was as close as Steve Bruce's side came until five minutes from time when Sagbo struck home after collecting a cross from Sone Aluko, making his first start after four months out with an Achilles injury.
Both teams had late chances to snatch victory, but Davies and Jake Forster-Caskey were both in the right place to clear headers off the line.
Saturday February 22
12:45 Chelsea v Everton
15:00 Arsenal v Sunderland
15:00 Cardiff City v Hull City
15:00 Manchester City v Stoke City
15:00 West Brom v Fulham
15:00 West Ham United v Southampton
17:30 Crystal Palace v Man Utd
Sunday February 23
13:30 Liverpool v Swansea City
13:30 Newcastle United v Aston Villa
16:00 Norwich City v Tottenham