Former world number one Sabalenka was forced to dig deep before finally prevailing 7-6(2), 7-5 in just under two hours.
Second-seeded Sabalenka is chasing her first-ever WTA Finals victory after suffering defeats in the 2022 and 2025 finals.
"I'm just trying to win every match I play, and at the same time trying to stay in the moment and focus on my game on each point and trying to stay calm and in control," Sabalenka said afterward.
The four-time Grand Slam champion from Belarus looked to be in trouble after conceding a break of serve to go 5-4 down in the opening set.
But Sabalenka broke back immediately for 5-5 and subsequently went on to hold her nerve in the tie-break 7-2 to seize the early initiative.
Both players struggled on serve in the second set, with Sabalenka suffering her fourth break as she served for the match at 5-4 up.
Crucially, though, Sabalenka responded to that stumble by breaking back immediately to lead 6-5, and she made no mistake when serving for the match again, wrapping up victory when Czech opponent Muchova netted a backhand.
Sabalenka and Muchova's group two duel was the first of two matches on Monday, with third seed Mirra Andreeva facing Elina Svitolina later in the day.
This year's WTA Finals were scheduled to be held in Saudi Arabia but in July were moved to Indian Wells after US military strikes on Iran in February and the subsequent war in the region.