He embraced Copil at the net after his 6-7, 6-3, 7-6 win and sat at his chair weeping for nearly five minutes.
He's scheduled to face 19-year-old Alex de Minaur of Australia in the quarterfinals Friday night. Murray recognised he had to prevent the aggressive player from playing his usual aggressive game, so Murray beat him with intent and beat him with depth.
Murray told reporters at the tournament: "I don't think it's reasonable and I'm disappointed in that". I don't think I should be put in a position like that, when you're expected to come out and perform the next day.
"Finishing matches at 3 in the morning is not good". I know that the weather's tricky for the scheduling. It's not good for fans, TV, nobody.
Strenigthened Category 4 Hurricane Hector Heads to Hawaii
Spaghetti models and charts show Hurricane Hector passing within a hairsbreadth of Hawaii's Big Island, where Kilauea rages on. The center of the storm was located about 1,360 miles east of South Point, Hawaii, as of the NHC's 2 a.m.
Murray was left sobbing after his marathon win over Copil in the early hours of Friday morning, which came after previous lengthy battles against Mackenzie McDonald and British number one Kyle Edmund.
He added: "There are lots of positives to take from this week, so I'll take some time to rest and recover - I won't play in Toronto next week - and then head to Cincinnati early to prepare and get ready".
Murray, playing only his third tournament since returning from hip surgery, criticised the "unreasonable" schedule of the hard-court event and has even threatened to withdraw from his last-eight meeting with the Australian world No 72.
"I'd obviously try and sleep as late as I can, but with the way your body clock is and stuff, you know, you might get a few hours' sleep".
Former world number one Murray, now ranked 832, denied Copil on all four break chances in the first set and took a 5-0 tie-breaker lead only to drop the next seven points and squander the set, yelling at himself several times before netting a backhand to end the misery. The Scot became overwhelmed with emotions and broke down in tears after embracing Copil at the net.