The defending champions benefited from goals in either half from Mandla Masango and Aubrey Modiba at Sugar Ray Xulu Stadium, earning Matsatsantsa their place in the quarter-finals.
But the victory was muddied by the late sending off of Thabo Mnyamane, who came on in the second half for goal scorer Masango, with the former University of Pretoria star lasting only 20 minutes before seeing red after stamping on a KwaDukuza player.
Baxter, who has won this competition twice - previously with Kaizer Chiefs in 2013 and last season with SuperSport in his first season in charge - said progressing was what mattered, considering the wholesale changes he made to the team ahead of their tough run of fixtures.
"It's a cup and the cup is about getting to the next round. We’ve got a lot of games [coming up] that we have to negotiate," Baxter said after the game.
"We’re changing and chopping the team very much and you lose continuity. So sometimes you take the result in the cup and move on.
"I thought we could've made it easy for ourselves but our lack of discipline, like Thabo and our lack of quality in certain areas didn't make the night an easy one. It could have been easy but we didn't make it easy and going to the next round is the bonus."
With a long trip to Liberia for their CAF Confederation Cup first-leg tie against Barrack Young Controllers on Sunday looming large, the former Bafana Bafana coach, who could return to the national team setup this year, said the plan now was to give his players plenty rest as he looks to keep the team fresh during their heavy run of games.
"We are going to rotate the team again," said Baxter.
“You can't have players coming off one game against Baroka [this past weekend] and playing [on Tuesday] then travelling 16 hours to Liberia and then coming back and playing [Mamelodi) Sundowns on April 13], you can't have the same players playing [all those games].
"So, we'll try and freshen it up and we left a few players out [against KwaDukuza] and I didn't really want to play Dean [Furman] but I had to.
"I had to tidy it up, especially when we were 10 men. So we'll recuperate some of the players and they'll go to Liberia and we'll give it a shot.
"We’re hoping to come back with a useful result so that we can play our next game [the second-leg] in Pretoria."