Murray, a 40th-ranked player from Britain, proved his mettle on the SW19 grass, leading 6-7 (3-7) 7-6 (7-2) 6-4.
Due to the limitations imposed by the local council, the second-round match was called at 22:39.
Murray and Tsitsipas, who have both played late in recent years, will pick up their exciting match on Friday.
Shortly after Murray, 36, finished the third set, tournament referee Gerry Armstrong entered the court and talked with each player about ending play for the evening.
The 24-year-old Tsitsipas promptly packed his bags as Murray, who cried out when he fell moments before serving out for the lead, informed his teammates that the match was going to end.
Following the first match, which begins at 13:30 and features Frenchman Alexandre Muller against top-seeded Carlos Alcaraz of Spain, the two will return to Center Court.
When the draw was announced last Friday, eyes were immediately attracted to this possible blockbuster.
Billed as the tournament’s box office encounter thus far, it came about after both players navigated their initial rounds in different ways.
