Frazer Richardson's glorious 53rd-minute strike put Leeds on course for victory before United deservedly hit back through Kabba with 21 minutes remaining.
Kabba's clinical strike ensured the Blades remain 12 points ahead of their Yorkshire rivals and prevented Leeds from recording three successive league victories for the first time since 2002.
United manager Neil Warnock took great delight in denying Leeds boss Kevin Blackwell victory following the pair's bitter fall-out after Blackwell quit Bramall Lane in the summer of 2003 to become Peter Reid's assistant at Elland Road.
Warnock was upset to learn from a journalist that his assistant was leaving and both men revealed on last April's meeting between their two clubs at Elland Road that they now rarely speak.
While there has since been a slight thaw in the cold war between the rival managers, on the pitch it was obvious from the outset that both sets of players were prepared to fight fire with fire.
United inflicted Leeds' worst home defeat in three years when they recorded an emphatic 4-0 victory at Elland Road in April, but there was no chance of such a scoreline this time around.
However, it was the visitors who almost drew first blood after eight minutes when Phil Jagielka's thunderous long-range strike sailed narrowly over.
United, fresh from their midweek 4-0 victory against Millwall, looked strong during the early exchanges before Leeds enjoyed a brief spell of sustained pressure which almost reaped dividends.
Eddie Lewis' dangerous low cross from the left flank narrowly evaded the lively strike partnership of Robbie Blake and Rob Hulse.
Hulse's neat turn and low shot from the edge of the box barely 60 seconds later flashed wide before Kabba emerged as a key threat for the visitors.
After 21 minutes, a delightfully-engineered move saw the ball played through to the United striker and his left-foot shot was beaten away by Leeds goalkeeper Neil Sullivan.
Kabba collected the ball again a minute later and hit a fierce strike from the edge of the box which forced Sullivan to tip over.
The pendulum swung back towards Leeds midway through the half when full-back Dan Harding cut in from the left flank and hit a superb right-foot shot which sailed just past Paddy Kenny's goal with the United 'keeper beaten.
Leeds came agonisingly close to the opener nine minutes before the break when Hulse headed Blake's cross inches wide at the far post.
However, the breakthrough arrived eight minutes after the restart when Blake collected the ball 25 yards from goal and found Richardson in support to his right.
The Leeds midfielder seized possession and smashed an unstoppable shot past Kenny to send Elland Road into raptures.
However, United hit back strongly and Kabba was on hand to claim a hard-earned point for his side after 69 minutes, driving low and hard past Sullivan from just inside the box.
Both sides pressed for a winner, but the respective defences held firm to ensure a deserved point apiece for the two promotion hopefuls.