The 24-year-old Greek won 3-6 7-6 (7-1) 6-2 6-7 (5-7) 7-6 (10-8) in a match that lasted three hours 56 minutes.
Novak Djokovic continued his pursuit of an eighth title by beating Australia’s Jordan Thompson 6-3 7-6 (7-4) 7-5.
Elsewhere, there were wins for American seeds Taylor Fritz, Frances Tiafoe and Tommy Paul, but Sebastian Korda lost.
Murray beat fellow Briton Ryan Peniston on Centre Court on Tuesday, one of only eight matches to be completed on day two.
The 36-year-old home favourite would have therefore been pleased to see fifth seed Tsitsipas involved in a gruelling encounter with 2020 US Open champion Thiem, played out over two days on a packed Court Two.
YOU CAN ALSO READ:Heartland Grab NPL Promotion
Austrian Thiem took the opening set on Tuesday and led 6-3 3-4 before rain meant the match had to be suspended and finish on Wednesday.
Tsitsipas took the second set on a tie-break, then the third to go ahead, but he lost the fourth set, also on a tie-break.
The deciding set went to a match tie-break and Tsitsipas, watched by girlfriend Paula Badosa in the latter stages after her own win, clinched victory at the second attempt after missing an earlier match point.
“I’m not expecting anyone to support me,” Tsitsipas joked before Thursday’s match against two-time champion Murray.
“Andy is someone who has done so much for the sport and and I have a lot of respect for the opponent I’m facing.”
Written by: Debby Eselebor
5:30 am - 10:00 am
Welcome to our extraordinary breakfast show, where the sun has just begun to peek over the horizon, and the world is ripe with endless possibilities. From the early hours of 5AM to 10AM on weekdays, we invite you to indulge in a symphony of captivating content that will set the perfect tone for your day.close