Having slashed ticket prices for the match, the promotion-chasing Blades guaranteed a bumper attendance of more than 27,000, but few in the ground will feel they had value for money after a turgid first half in which the visitors more than held their own.
But the same cannot be said for a pulsating second period in which goals from captain Phil Jagielka, Paul Ifill and a first of the season for Michael Tonge wrapped up the points before substitute Colin Kazim-Richards netted a consolation for struggling Albion.
Top scorer Kabba replaced the injured Danny Webber in the United starting line-up, while Craig Short made his first appearance for five weeks, preferred in defence to club captain Chris Morgan.
Brighton understandably made no changes from the side which beat Leeds 2-1 last weekend and they began confidently, creating the first opportunity when Sebastien Carole's trickery and cross set up Gary Hart, who failed to connect properly with his head.
Playing on the counter, Albion almost broke the home offside trap minutes later but Hart was too quick off the mark onto Paul Reid's ball.
Despite committing plenty of bodies forward United's passing lacked any real urgency and it took a set-piece to create their first chance, David Unsworth's inswinging free-kick prodded wide by Kabba.
Another set-play, and another opportunity, with Unsworth's corner nodded back by Neil Shipperley but put behind by Brighton captain Guy Butters.
Then out of nothing, Kabba rifled a shot towards Michel Kuipers' near post with the keeper parrying straight to Ifill, who somehow hooked the rebound wide.
United were rescued by the offside flag again when Carole broke through, while Alexandre Frutos almost deflected Derek Geary's cross into his own net.
Jagielka then headed Leigh Bromby's long throw straight into the arms of Kuipers, who was not enduring the busy afternoon he might have anticipated.
What can only have been a half-time rollicking from manager Neil Warnock appeared to have the desired effect, with the deadlock broken eight minutes after the restart.
Chris Armstrong had two attempts to cross, the first blocked, but the second finding the left foot of Jagielka, whose hooked volley left Kuipers motionless.
Albion boss Mark McGhee's response was almost immediate, Kazim-Richards coming off the bench and into the attack.
But United had upped the tempo and Jagielka tried his luck from range before Ifill made up for his earlier miss with a piece of opportunism to make it 2-0.
Young Albion left-back Joel Lynch was guilty of dwelling on the ball and Ifill pounced, nicking the ball before cutting inside and clipping the ball over Kuipers.
Unsworth whipped in another dangerous free-kick just too high for Short and Ifill's lovely skill made space for a blistering strike Kuipers could only parry.
And Ifill was involved in a brilliant third, his long diagonal ball played on perfectly by Kabba into the path of Tonge, who burst clear and finished low to Kuipers' right.
With the game won, Warnock introduced 37-year-old Brian Deane for his third 'debut' for the club, almost 18 years since his first appearance for the club.
The party mood was dampened somewhat by a spat between Kabba and Albion's Paul McShane, and was not improved when Kazim-Richards pulled one back with a low angled drive which appeared to take Paddy Kenny by surprise.
But Deane nearly stole all the headlines when he got a trademark header to fellow substitute Alan Quinn's cross only to be thwarted by Kuipers.