The hosts made their intentions clear from the start, looking for combinations in the midfield and exploiting the pace of Sifiso Myeni and Vincent Pule on the wings, while Celtic looked to play through Deon Hotto with the long ball over the top.
Patrick Tignyemb was good between the sticks for Celtic all evening, making his first telling save to deny Lehlohonolo Majoro’s header from close range.
Majoro looked lively, almost carving out an effort minutes later, the visitors defence doing well to close him down and snuff out the chance.
The hosts made their superiority pay on the half hour mark. Mpho Maruping conceded a penalty and was shown red for a deliberate handball to divert a goal-bound effort.
James Keene stepped up and sent Tignyemb the wrong way, drilling his spot-kick into the roof of the net.
The Free State side looked for a way back into the match by way of substitutes, introducing Menzi Masuku early in the second stanza.
Gavin Hunt made changes of his own to secure the result, introducing ball players Monare, Klate and Pelembe to ensure the hosts could dictate the pace.
Daylon Claasen was at the heart of the Bidvest Wits midfield, working hard at the back and looking to create chances as The Clever Boys pushed forward. He did well to keep a ball alive and play in Majoro 20 minutes before full time, the latter just ahead of the delivery and unable to convert.
Hotto looked to push until the final whistle and was almost rewarded as he was picked out. The Namibian controlled the ball on his chest, turned and shot but his effort was wide of Darren Keet’s goal.
Hunt will hope his charges have turned the corner, and look to build on an unbeaten run of three games in the league.
The result sees Bidvest Wits move into 13th, while Celtic’s run on the road continues to cause concern for Veselin Jelusic.