Wits got themselves onto the scoresheet twice in the opening stanza as Buhle Mkhwanazi netted the opener and Daine Klate doubled the advantage with a fine half-volley.
Mkhwanazi grabbed his brace with another headed effort in the second period and Ejike Uzoenyi and Phakamani Mahlambi put gloss on the result as Wits coasted to victory against a Baroka side that looked out of their depth.
Bakgaga looked shaky in the opening stages of the match but grew in confidence as the minutes progressed and looked as though they may have been up for the challenge.
They will feel they should have gone ahead midway through the half but Nyasha Munetsi missed a gilt-edged opportunity midway through the first-half.
In the 31st minute a brilliantly worked freekick saw the centre-back pairing of Thulani Hlatshwayo and Mkhwanazi combine before the latter stooped to head home past Avhashoni Tshinuna.
With the opening half hour having been largely bereft of Wits chances they had another only a matter of minutes after their opener and it too was duly buried.
The main orchestrator of the goal was Gabadinho Mhango who took two touches to engineer space in the box before using his third to delicately lift the ball to Klate to finish with aplomb.
Approaching the hour mark Klate surprised everyone in the ground when he unleashed a vicious strike from range using his right-foot and the 'keeper had to palm it behind.
The introduction of Mahlambi resulted in a goal as the young forward delivered in a peach of a cross that Mkhwanazi deposited into the net via his head.
Things went from bad to worse for the visitors as another substitute in the shape of Uzoenyi got amongst the goals as he slammed home at the near post.
Just to add insult to injury Mahlambi chipped in with a goal of his own as he nudged the ball past a defender in the box before sliding it home brilliantly.