The deadlock was broken when Shaun Derry released Robbie Blake, whose square pass enabled right-back Richardson to pass Alan Wright as if he wasn't there before unleashing an unstoppable drive from just inside the penalty box.
The equaliser arrived on 69 minutes when substitute Danny Webber wrong-footed the Leeds defence and shuttled the ball to Kabba who beat Neil Sullivan with a low shot into the left corner from 12 angled yards.
Leeds gave central defender Matthew Kilgallon only his second league start of the season to counteract Kabba's pace, with Sean Gregan dropping to the bench and losing his ever-present record.
The Blades made five changes from the side which thrashed Millwall 4-0, including the recall of strikers Kabba and Neil Shipperley.
Smarting from last season's 4-0 defeat against the Blades at Elland Road, Leeds fought for every ball in a Yorkshire derby which never stopped for breath.
Kabba forced Sullivan to make two smart saves in the opening 25 minutes but Blake was sharp in the Leeds attack and when Dan Harding cut inside, the left-back's power-packed shot was only fractionally too high.
Referee Alan Wiley was determined to ensure the importance of the occasion did not spark trouble and cautioned Gary Kelly and Rob Hulse for first-half offences.
The best chance of the half fell to Hulse on 36 minutes, when he met Blake's deep cross at the far post but headed just wide when he should have scored.
Phil Jagielka made some powerful runs from Sheffield's midfield but the Blades' forwards struggled to find a cutting edge
Visiting manager Neil Warnock responded to Richardson's goal by replacing the ineffective Paul Ifill with Keith Gillespie, who was on trial at Leeds in pre-season.
Then Webber took over from Shipperley and promptly wasted a clear chance by mis-kicking before atoning by setting up Kabba's leveller.