Trailing the log leaders by six points heading into Wednesday's tie, Chiefs needed all three points to keep the pressure on the Brazilians, who now lead the defending league champions by five points, having played a game more than the chasing Amakhosi.
With the top three all but secured already, Wits did little to change their fortune and look destined for a third-place finish to the season, a place better than last season's surprise top four finish.
The mouth-watering encounter between two of the country's front-runners produced end-to-end action from the first whistle, Lebese trying his luck from distance, before a promising corner caused problems for the Chiefs defensive unit shortly after.
The Clever Boys looked up for it and forced a spectacular save from Chiefs goalkeeper Itumeleng Khune in the 16th, the Bafana Bafana number one pulling off a stunning effort to his left to deny Sthembiso Ngcobo who got a shot away from a tight angle inside the Chiefs area.
The visitors replied with a chance of their own, as Parker dispatched a powerful free-kick at goal, but Wits shot-stopper Moeneeb Josephs was left with a straightforward parried save.
The resulting throw-in led to a clinical break from the hosts, who drew a corner, after Vilakazi's good work in the area handed Wits another shot on goal.
Wits kept up the pressure and continued to trouble Chiefs from the set-piece, which allowed the home side to create a host of chances, Ngcobo grazing the top of the crossbar shortly before half-time.
Level at the break, the Students started the second period much the way they did the first and went dangerously close through Asive Langwe on the left, the winger thundering against the upright following some good work by Vilakazi down the middle, which would have capped a superb goal, were it not for the intervention of the woodwork.
When Wits eventually found the back of the net after the hour mark, referee Victor Gomes ruled Ngcobo offside, while at the other end, Josephs was a mere spectator.
The disallowed goal was testament to Wits' dominance and did little to spark Chiefs into life. They came closest after the break from a throw-in, which Kingston Nkhatha ballooned over the crossbar when the ball came down, as Chiefs began to run out of time to grab maximum points.
Chiefs brought on Katlego Mphela late on and his impact was immediately felt, as the former Downs attacker struck the crossbar from close range, in a cruel denial of what would have surely sealed a last gasp winner for the Amakhosi.
Mphela's near-miss was followed by an even closer chance, as Josephs came to the rescue and kept Erick Mathoho's attempt off the line in the closely-contested affair in front of a packed Wits crowd, who braved the cold and watched as the league came a game closer to being decided.