Ukrainian veteran Svitolina lifted the WTA Finals trophy in 2018 but hadn't been back to the elite season-ending event since 2019.
She got off to a rocky start against Muchova, who broke Svitolina three times in the opening set.
Trailing 2-1 on serve in the second, Svitolina found her range, winning five straight games to force a third set.
"I was not happy with the first set," Svitolina said. "I didn't play as well. I just made some adjustments, tactical adjustments.
"I tried just to go more for my shots because I played kind of with her game," she added. "She has an amazing variety of the shots with the slice, with the serve and volley. I had to stay away from that and try to find shorter balls earlier in the rally.
"I think it helped me also to be more aggressive, because I was too passive in the first set," Svitolina said.
Svitolina said she was able to channel her "angriness" that had been brewing since her straight-sets loss to Mirra Andreeva in her round-robin opener.
She handed Muchova a second defeat in round-robin play and improved to 1-1 and will have a chance to compete for a semi-final berth when she takes on world number two Aryna Sabalenka of Belarus in their final group match on Friday.
Sabalenka took on third-seeded Russian Mirra Andreeva in Wednesday's other group match.