The No. 10 seed Tsitsipas beat No. 3 David Goffin 6-3, 6-4. The 31-year-old is expected to play in Cincinnati.
The Zverev-Nishikori result was delayed for more than two hours by rain with Zverev leading 3-2 with a break in the third set.
After playing until 3 a.m., then sobbing into a towel, Andy Murray made it clear he was not pleased with the prospect of having to play again so soon.
The 31-year-old British star, who returned in June from an 11-month layoff with a right hip injury, also withdrew from next week's ATP Toronto Masters, also citing the drain from three gruelling three-set victories over more than eight hours on the USA capital hardcourts.
Three-time Grand Slam champion Murray, in his first hardcourt event after an 11-month layoff for a right hip injury, outlasted Romania's 93rdranked Marius Copil 6-7 (5/7) 6-3 7-6 (7/4).
Andy Murray has withdrawn from his Citi Open quarter-final after a late-night finish on Friday morning. "It's not good for the players".
"I don't think I should be put in a position like that", Murray said after the victory. "Not good for fans, not good for TV, nobody".
If Murray came to Washington in hopes of getting in some extra work as he tries to return to form after hip surgery in January, he is certainly accomplishing that.
"I've played quite a few matches this week in Washington and I need to be smart with my rest and recovery as I come back from injury", he said.
Tournament Director Keely O'Brien added: "I am so grateful that Andy, an incredible champion, came back to D.C.to begin what we all know will be a great comeback. I don't think it's reasonable", Murray said.
"I do understand 3 a.m.is very hard for everyone", O'Brien said.
Earlier he had criticised the scheduling of matches.
Asked after beating Copil how his body is holding up, Murray replied: "It doesn't feel great, just now". By the time you're done with all your recovery and stuff, it's going to be 5:30, 6 o'clock in the morning. On Monday, he didn't play his opening-round match until 10pm because of a five-hour rain delay.
Murray - now ranked 832 in the world - lost the first set against Copil in one hour and six minutes, having taken a 5-0 lead in the tie-break before losing seven points in a row.