Zverev, coming off what he had described as one of his worst matches of the season in his opening loss to Medvedev on Monday, led 3-1 in the second set before his Argentine opponent battled back with two breaks.
The 23-year-old has not yet won a major but reached the semi-finals of the Australian Open this year and the final of the US Open.
"Since the restart it was one of my worst matches", Zverev, who will need to beat Schwartzman on Wednesday to stay in the hunt, told reporters. Only one of their six previous encounters has ended in straight sets and the last three have all required final sets.
In a repeat of last year's final at London's O2 Arena, won by Tsitsipas, US Open champion Thiem stumbled after winning a first-set tie-break but found his range again to win 7-6 (7/5), 4-6, 6-3.
'I'm happy that I got it today'.
The unforced errors were mounting for Schwartzman and Zverev made him pay, winning four games in a row and wrapping up the set when the Argentinian sent a forehand beyond the baseline at full stretch on the run.
The top-ranked Djokovic smothered Schwartzman after conceding an early break and, despite no fans inside the 20,000-capacity O2 Arena, he gestured to each section as if to say thanks.
Thiem will be the first player to qualify for the semi-finals if Tsitsipas defeats Rublev in the late session. "I was very pleased with the way I played". Nadal won his first round-robin match against Andrey Rublev on Sunday at the ATP Finals.
"My wide serve was not working as well as I would like and he was returning good", Medvedev said. "It's part of the game that I want to play against Rafa".
"I said from the beginning of the week that I'm going to improve with every match, because after the small injury I had in Paris, I needed to recover a little bit and get back into the rhythm". A serve-volley on second serve saved him but Theim would eventually earn his sixth career win over Nadal in the ensuing breaker.
The world number one wobbled at the start of the match against the diminutive eighth seed, making his debut at the elite eight-man event but recovered to win 6-3, 6-2.
The win moves Thiem to 2-0 in the London Group. "I think my chances are bigger to have a very good result now than five days ago because the level of tennis, even if I lost today (against Thiem), for me, is much higher", said the joint-record 20-time Grand Slam victor, who has a 5-1 advantage in head-to-head meetings with the Greek.
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