Late substitute Ibra Sekajja scored an 88th-minute equaliser as Crystal Palace retained their Championship status for another season.
Anthony Gerrard gave Hull the lead from close range after Jack Hobbs headed Robert Koren's free-kick across goal.
Palace were then obliged to weather a storm as Aaron Mclean, Koren and David Amoo all went close for the home side.
But with two minutes left, Sekajja sent a cool finish beyond Hull keeper Matt Duke from Claude Davis's cross.
It was a memorable moment for the youngster, who scored with his first touch in professional football. He started the season in Palace's academy side.
The afternoon was equally memorable for Eagles boss Dougie Freedman, who has overseen steady progress since his appointment last November, when the Eagles were languishing second from bottom of the Championship table.
In confident mood after their Easter Monday victory over promotion-chasing Leeds, the visitors enjoyed the better of the opening exchanges.
Hull, whose own play-off dreams were snuffed out over the Easter period, started slowly and were further hampered when Richard Garcia was forced off with an ongoing knee injury after just 14 minutes.
Darren Ambrose went close for Palace, drawing a fine save from Duke with a free-kick, but Hull gradually shook off their torpor before Gerrard's simple finish gave them the lead.
Palace keeper Julian Speroni subsequently thwarted Mclean with a fine save, and the home pressure continued after the break as Koren volleyed over before Amoo sent an effort just wide.
But with two minutes to go Sekajja struck to condemn the Tigers to the 17th league draw of their campaign.