Former world number one Murray, who skipped Wimbledon as he continues his return from a hip injury, has now ground out a trio of three-set victories in Washington DC this week. "Not good for fans, not good for TV, nobody".
The former world No. 1 - now ranked 832nd - took out Copil 6-7 6-3 7-6 to set up a clash with Aussie youngster Alex de Minaur in what will be his first quarterfinal in over a year.
"It was just the emotions coming out at the end of an extremely long day and a long match", Murray told reporters. "And I'm disappointed with that, because I know that the weather's tricky and I know it is for the scheduling, but it's a very hard position to be in".
But the Romanian immediately broke back before holding serve to level the match, before Murray's fitness prevailed in the deciding tie-break.
The 31-year-old was left sobbing in his chair after overcoming the latest three-set marathon of the tournament.
Falling a set behind appeared to spark Murray to life and he grabbed an early break in the second against the world No. 93.
The Brit will next take on Alex De Minaur on Friday with only a few hours to rest up before their last-eight clash. He will face Italy's Fabio Fognini for a place in the final.
The pair shared breaks in the third set, and as the clock ticked on later into the night, Murray eventually emerged victorious (7-4) in the final tie break - at 3:01 a.m.
Norrie won almost three-quarters of his first serve points as he dismissed the fourth seed and world number 25 to reach his second successive ATP Tour semi-final.
Heather Watson took Venus Williams to three sets before succumbing 6-4 4-6 6-0 at the Mubadala Silicon Valley Classic in San Jose.
"It's basically like playing two matches in a day". 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. "It worked out, thankfully".