The game appeared destined for a goalless draw as both sides missed a bucketful of chances, but Simpson, an 80th-minute replacement for Aaron Mclean, lashed the ball high into the roof of the net from inside the penalty area to deny Brighton a share of the points they deserved.
Simpson, whose last goal for the Tigers was in April 2011 against Middlesbrough, twice went close to adding a second goal in the 90th minute, but was denied by sprawling Brighton goalkeeper Tomasz Kuszczak, while blazing another effort over the crossbar.
Hull earlier hit the woodwork through summer signing Sone Aluko, but the scoreline was rough justice on Gus Poyet's Brighton, who took the game to their hosts for long periods and spurned numerous clear-cut chances, with Craig Mackail-Smith heading against the crossbar early in the second half.
Brighton striker Ashley Barnes headed the game's first chance over the crossbar in the fifth minute, but Hull went closer to taking an early lead soon after when Aluko's curling shot from 20 yards was well saved by Kuszczak, a free capture from Manchester United.
Brighton midfielder Craig Noone sent a shot from outside the penalty area fizzing wide and then crossed for Mackail-Smith, who headed just off target in the 21st minute, as Poyet's side began to look dangerous on the counter-attack.
Hull had to wait until the 30th minute before their next opening, midfielder Robert Koren crashing a 20-yard shot straight at Kuszczak.
Brighton wrestled back a more equal share of possession as half-time approached and another summer signing, Andrew Crofts, fired a shot inches wide.
Hull were then denied by the woodwork in the 35th minute when Aluko's cross-cum-shot from the left beat Kuszczak only to rebound back off the crossbar and the Brighton goalkeeper was at his best moments later when diving low to turn away another thumping drive from Koren.
Paul McKenna almost broke the deadlock in spectacular style four minutes into the second half when he crashed a shot from 30 yards towards the top corner, but Kuszczak was equal to it again and tipped the ball over.
Then it was Brighton's turn to be denied by the woodwork. Noone crossed after another sweeping move and Mackail-Smith headed the ball against the crossbar in the 50th minute.
Noone curled a shot wide and midfield team-mate Gary Dicker headed Wayne Bridge's cross narrowly off target, while at the other end Koren dragged his effort wide and home appeals for handball were turned away by referee Stuart Attwell when Aluko's shot was blocked by Crofts in the area.
Mackail-Smith pulled his angled volley wide and Hull goalkeeper Ben Amos did well to keep out Kazenga LuaLua's 25-yard shot with 10 minutes to go, but substitute Simpson converted high into the net from defender Joe Dudgeon's pass and was then denied by another superb save from Kuszczak when he looked poised to make it 2-0 in the closing stages.