Third-ranked defending champion Alexander Zverev took bragging rights in his sibling rivalry, beating 15th-seeded older brother Mischa 6-3, 7-5 in their first ATP meeting.
Murray was playing in just his third event since having hip surgery previous year.
It was Murray's first hard court tournament since March 2017 having been plagued by a hip injury.
Now ranked 832nd, Murray ended an 11-month absence from the tour in June, playing just three matches before arriving at the Citi Open.
Defending champion and world number three Alexander Zverev of Germany was set to face Japanese seventh seed Kei Nishikori, with the victor to face Tsitsipas, and local hero Denis Kudla was to meet Russian 16th seed Andrey Rublev in other quarter-finals.
De Minaur will next play either Russian 16th seed Andrey Rublev or American Denis Kudla, whose match was postponed to Saturday, among with three women's quarter-finals, by a fifth consecutive day of rain.
Murray had earlier announced he would not be playing in next week's Rogers Cup, which would have been his first Masters tournament since last spring. Murray's withdrawal, announced earlier on Friday, gave Australia's Alex de Minaur a free pass to the semi-finals where he will meet the victor of Andrey Rublev and American Denis Kudler. "I'm not sure how well I'll recover from that".
All tennis fans rejoiced at his pain-free movement and fitness levels shown to win three such draining matches.
2 dead, dozens injured in explosion on highway near Bologna, Italy
The accident was similar to one on Saturday, when a truck laden with tomatoes crashed into a white van and four migrants died. Italian police posted a video showing the damage down to the bridge after the blast, showing a crater in the road.
"I don't think I should be put in a position like that", Murray said.
It has been a tortuous year for the 31-year-old, watching helplessly from the treatment table as he plummeted down the rankings while his hip condition worsened to the extent that surgery was required in January. "I don't think it's reasonable", Murray said.
"I do understand 3 a.m.is very hard for everyone", O'Brien said.
"I'll try to sleep as late as I can but with your body clock you might get a few hours sleep".
He declared in a statement: "I won't be able to play my match tonight".
Murray looked set to win the opening set against Copil, ranked 93, after moving 5-0 ahead in the tie-break only for the Romanian to reel off seven points in a row.
When he got to the sideline after the match concluded, he covered his face with a towel and cried, his chest heaving.
The match eventually finished at 3am on Friday morning and Murray shed tears into a towel for several minutes courtside as the emotion of the moment overcame him.