Bongani Ndulula had fired the hosts in front after 22 minutes of a first half dominated by the hosts, before Lebese drew his side level with a lifted finish on the hour.
The Amakhosi midfielder then converted from close range, as the game entered the 94th minute following a free-kick that came back off the left upright by Siphiwe Tshabalala to extend Chiefs’ lead at the top of the table to 11 points.
AmaZulu began brightly and could have been ahead inside four minutes as Sifiso Hlanti dinked over an inviting left-sided cross for Ndulula, who had little time to react as his point-blank effort was blocked by goalkeeper Brilliant Khuzwayo.
Chiefs responded through slick attacking moves through the middle, the first ending with Lebese miscontrolling and the second saw Mandla Masango fire inches over.
At the other end, Hlanti was causing more problems down the left and set up Bornwell Mwape for an angled shot, which was blocked by Khuzwayo.
When Amakhosi ventured forward the next time, Tshabalala watched his strike from the edge of the box deflect inches wide.
Usuthu then took the lead against the run of play midway through the half as Mwape and Goodman Dlamini had a big hand in the opener — the former saw his shot cannon back off the left upright and latter’s effort was parried by Khuzwayo into the path of Ndulula to crash in.
The championship pacesetters tried to find a response but were constantly poor in the final third as their strike-force failed to fire. Before the break, though, Bernard Parker did have a chance that was wasted as the Bafana Bafana front man dragged his shot wide.
It remained 1-0 at the break and after the restart the home side had further chances to stretch the lead.
Nkosinathi Mthiyane blasted over in the 48th minute, before Mwape forced Khuzwayo into a low save to his left with an ambitious shot from the left.
Chiefs were rocking at that stage, but they came close to a goal of their own when Tshabalala’s effort from outside the box forced Kapini to push wide, before the equaliser arrived on the hour.
It came when Reneilwe Letsholonyane and Tshabalala combined to put through Lebese, who lifted beyond the helpless Tapuwa Kapini from just inside the box.
And Chiefs almost took the lead eight minutes later when Masango’s header came back off the right upright from a Siboniso Gaxa cross, with Kapini scrambling away the rebound.
But the winner arrived at the death as Kapini could only watch Tshabalala’s free-kick outfox him and leave the goal clear for Lebese to fire in.