With the Telkom Knockout semi-final defeat still fresh in their minds, Wits were out to avenge that particular defeat and started by attacking with numbers.
Their first chance at goal inside the opening 10 minutes after Gabadinho Mhango found space on the left to cut into the box before getting a shot away which found the side-netting.
Baroka were not too overawed and found a few spaces behind the Students defence with a few of their penetrative passes, but their front-men were unable to capitalise.
There was to be another good chance falling in the path of Wits after the earlier pressure from Baroka, as a long ball from Deon Hotto found Mhango who failed to keep his effort on target.
Baroka’s first shot on target was presented by Jemondre Dickens who turned to get a low effort away following a pass from midfield but Keet was able to get down to make the save.
On the stroke of halftime, Wits broke free through Lehlohonolo Majoro's clinical finish that left Elvis Chipezeze with no chance.
Baroka were hoping to get a quick response in the second half, but a header from Dickens was only able to find the side-netting in the opening five minutes.
Wits made it 2-0 after 59 minutes after Hotto was left unmarked to volley home a low pin-point cross from Elias Pelembe.
The goals seemingly knocked the sail out of Bakgaga, who were down and out in trying to orchestrate a way back in to the contest.
With time running out, Chipezeze came up trumps to stop Mhango from finding the near post before gathering safely on the follow-up to deny a lurking Majoro.
Bakgaga set-up a nervy ennding after Tebogo Sodi crept inside the box to bundle the ball home, following a cross from Thabiso Semenya 10 minutes to full-time.
Despite the late pressure, Bakgaga were unable to force a draw as Wits held on for three points to leapfrog Orlando Pirates into top spot.