The hosts dominated possession in the early stages but they rarely threatened and it was Hull who came the closest to opening the scoring, with Sagbo clipping the crossbar with an improvised effort after Ahmed Elmohamady's cross from the right.
However, Brighton did take the lead on the 30-minute mark as Leonardo Ulloa exchanged passes with Will Buckley inside their own half before the striker raced through on goal to calmly slot past Allan McGregor.
Hull almost responded immediately but the woodwork denied them for a second time of the evening as Curtis Davies saw a towering header kept out by the post and neither Sagbo nor Elmohamady were able to capitalise on the rebound.
After the break, the Tigers pushed for an equaliser, throwing on striking duo George Boyd and Matty Fryatt, but it was Sagbo who got the crucial goal as he fired home from close-range after Sone Aluko found him in the area.
David Meyler could have won it late on for the visitors but Jake Forster-Caskey was on hand to clear his bullet header off the line following Tom Huddlestone's corner.
Given the number of changes made by both teams, it was little surprise that it took a while for the match to get going.
Albion edged the opening 20 minutes but were struggling to create clear-cut chances, with Forster-Caskey hitting wayward efforts either side of an equally off-target Buckley strike.
A tame Sagbo attempt was all Hull could muster until the 27th minute, when the powerful striker met a cross from the right with an unorthodox volley that rattled the underside of the crossbar.
The effort started an exciting period in which Brighton broke forward to net a stylish opener.
Having started the move with a neat flick to Buckley, forward Ulloa collected the return ball and burst forward on goal, continuing to delicately lift over the onrushing McGregor.
It was a wonderful team goal by the hosts and one that was so nearly chalked off immediately as Huddlestone's corner was directed onto the crossbar by Davies. Sagbo's follow-up looked set to be turned into his own goal by Matthew Upson, only for goalkeeper Brezovan to save his blushes.
Play was delayed after Adam Chicksen collided with Davies, before Ulloa had the home fans on their feet in stoppage time.
Unmarked, he met a fine right-wing cross with a powerful header that rippled the net - although it quickly became apparent that it had only done so after going narrowly wide and rebounding off the stanchion.
Solly March replaced Buckley when the teams returned for the second half, with the midfielder welcomed to the fray by a challenge that earned Hull captain Robert Koren a yellow card.
City were struggling to create much on the attack and brought on Boyd and Fryatt shortly after Keith Andrews turned behind a fizzing Huddlestone free-kick.
The changes did not have the desired effect, though, with Inigo Calderon having efforts either of a poor March strike as Brighton looked to double their advantage.
Hull were becoming desperate in their bid to level, with Fryatt and Huddlestone leading the visitors charge without success.
The 695 travelling fans continued to gee on their side as the match entered the closing stages and got their reward with five minutes left.
Aluko whipped in a hopeful cross from the right, which Sagbo controlled under pressure and slotted through Brezovan's legs.
Both sides had wonderful chances to win after that, with Brighton seeing a goalbound header cleared off the line by Davies before City came close at the other end.
Koren saw a late short deflected for Bruce's side, before Forster-Caskey cleared substitute Meyler's header off the line.