Three-time Grand Slam champion Murray, in his first hardcourt event after an 11-month layoff for a right hip injury, outlasted Romania's 93rd-ranked Marius Copil 6-7 (5/7), 6-3, 7-6 (7/4).
The 31-year-old Scotsman won his third three-set victory in four days, having been on the court for eight hours 11 minutes in all, and he started at midnight thanks to a fourth day of rain delays, AFP reported.
"I don't think I should be put in a position like that," Murray said. "(My body) doesn't feel great right now.
"I've had a few long matches. Finishing matches at three in the morning isn't good for anyone involved in the event, players, TV, fans, anyone.
"When you're expected to come back and perform the next day, I think that's unreasonable."
And the sheer lateness of the hour wasn't good for players.
"That's something the tour needs to look at," Murray said.
The British star said he was unlikely to finish post-match conditioning and get to sleep before 5:30 a.m., ahead of a scheduled Friday quarterfinal against 19-year-old Australian Alex De Minaur.
"Not playing, potentially, is possible. I don't know how players are expected to recover from that," Murray said.
"It's like playing two matches in a day. I'm not sure how well I'll recover from that."
After the final point, Murray went to his chair, buried his face in a towel and wept, sobbing at times, and kept his head down and face covered as he exited the court.
"Not a whole lot, really, the emotions coming out at the end of an extremely long day and a long match," Murray said of what made him so emotional.