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Amakhosi romped to a 2-0 lead after 36 minutes, following a brace from in-form striker Bernard Parker.
The Clever Boys were able to pull a goal back before Lehlohonolo Majoro sealed the win as Chiefs drew further clear at the top of the league standings.
"I thought we were outstanding," Baxter said.
"Our forward play, our transition play and our possession was tremendous in the first half."
With the crowd attendance at over 30 000 at Mbombela Stadium, the game saw more than three times the number of fans than for the Bafana Bafana friendly against Mozambique less than two weeks prior at the same venue.
The spectators were treated to a more even contest in the second period when Chiefs failed to show killer instinct in finishing off their opponents and allowed Wits back into the game.
"In the second half we came out cold. We didn't get our game together," Baxter said.
"Wits upped their game a little bit, they played a bit longer, put more pressure on us, and for 20, 25 minutes I was going hysterical on the bench.
"I just wanted us to get back to playing.
"And because they were pressing us we had the opportunity for some great transitions but we didn't take it, so they got to 2-1 and we were all a bit unnerved for a few minutes."
After five Premiership games in charge of the Soweto giants, Baxter had guided the side to a five-point lead at the top of the table, with 13 points, after the first of a full round of mid-week matches.
Parker lifted his goal tally to seven strikes in the league campaign, but Baxter praised the efforts of the entire squad without singling out individuals.
"The players did a fantastic job in terms of their application in the moment - application in training and also during games," he said.
"We have a squad with a few injuries - a few important players - but the way the squad reacts to these injuries, I like it, it's very mature."
