The 36-year-old twice former champion, who plays with a partly metal hip joint, rolled back the years to lead 6-7(3) 7-6(2) 6-4 when play was stopped with the 11pm curfew looming.
Few players can engineer drama like the Scot and he had a soccer-style crowd screaming their lungs off as he went toe-to-toe with the fifth-seeded Greek in a match of stunning quality.
After a soggy opening three days of the championships which meant 17 first round matches were still to be completed on day four, the tournament caught fire as the rain finally departed.
Swiss veteran Stan Wawrinka, (38) who like Murray has three Grand Slam titles to his name, earlier produced vintage form to knock out 29th seed Tomas Martin Etcheverry 6-3 4-6 6-4 6-2 and set up a third-round clash with reigning champion Novak Djokovic (36).
Women's title holder Elena Rybakina (24) battled past France's Alize Cornet (33) 6-2 7-6(2) to reach round three while Ukraine's Elina Svitolina (28) continued her dream return to the Tour after becoming a mum to edge out 28th seed Elise Mertens (27).
But the day's unlikely lad was British wildcard Liam Broady who produced the biggest shock so far in the men's draw, putting out Norway's fourth seed Casper Ruud (24) in five sets.
Left-handed journeyman Broady, ranked 142nd in the world, lit up the afternoon with a 6-4 3-6 4-6 6-3 6-0 defeat of Ruud in front of a delirious Centre Court crowd.
Ruud had reached three of the last five Grand Slam finals including at Roland Garros last month whereas Broady's 10-year professional career had never seen him crack the top 100.
After four closely-fought, if erratic sets, Ruud, who spent the three weeks since reaching the French Open final relaxing away from tennis, looked like he had mentally packed his bags again as Broady ripped through the decider for a memorable win.
"It's a pretty terrifying, exhilarating experience, coming out on Centre Court at Wimbledon. It's been my dream since I was five years old," Broady said in an on-court interview.
Wawrinka will face Djokovic for the first time on grass on Friday having beaten him to win the 2015 French Open and 2016 U.S. Open, although he has lost 20 of 26 meetings with the Serb who is bidding for a fifth Wimbledon title in a row.
"There's zero opportunity to win Wimbledon for me, I think. I'm happy to have won today again. It was a great match. It's an honour to play Novak here," Wawrinka said.
"I was missing that in my career to play him in the Grand Slam in Wimbledon. Hopefully, I can make a competitive match, but if you will look at recent results I don't stand a chance."
ABSORBING DUEL
Logic suggested Murray would be a heavy under-dog against Tsitsipas too having struggled to reach his former heights since career-saving hip resurfacing surgery in 2019.
But after losing a tight opener against the elegant Tsitsipas he produced tennis few thought he was still capable of to level the match and then win the third set.
The crowd had their heads in their hands, however, as on Murray's second set point at 5-4 in the third he fell to the ground clutching his groin, apparently in agony.
He got back to his feet, however, and clinched the set and an absorbing duel will continue on Centre Court on Friday, although how mobile he will be is nobody knows.
Serbia's Laslo Djere (28) awaits the winner.
Tuesday's near wash-out and Wednesday's showers meant former world number two Alexander Zverev (26) hit his first ball in anger on day four, but made up for lost time with a 6-4 7-6(4) 7-6(5) win over Dutch qualifier Gijs Brouwer (27).
Rybakina looked for all the world a defending champion as she swiped winners for fun in a 26-minute first set against Cornet but her game cooled off rapidly and she was relieved to survive an 82-minute second set.
She will next face Britain's Katie Boulter (26) who ensured the home nation retains an interest in the women's draw with a three-set victory over Viktoriya Tomova (28).
Fifth seed Frenchwoman Caroline Garcia (29) also reached round three as she edged past 2021 U.S. Open runner-up Leylah Fernandez (20) thanks to a third-set tiebreak.
Swiss 14th seed Belinda Bencic (26) also needed a third-set tiebreak to fend off American Danielle Collins (29) but fourth seed Jessica Pegula (29) of the United States proved far too good for Spain's Cristina Bucsa.
The former semi-finalist won a topsy-turvy clash against Mertens 6-1 1-6 6-1 and will next face resurgent American Sofia Kenin (24) after the former major champion eased past China's Wang Xinyu (22).
Former men's runner-up Matteo Berrettini (27) was among those who moved belatedly into the second round as he sealed a 6-7(5) 6-3 7-6(7) 6-3 win over fellow Italian Lorenzo Sonego (28) in a first-round match that spanned three days.
