Third-seeded Murray, who snapped Britain's 76-year wait for a men's Grand Slam champion when he triumphed in New York last year, needed just 98 minutes to get past 33-year-old Frenchman Michael Llodra, 6-2, 6-4, 6-3. (Agencies)
But his match only got underway at 9:55 pm (0155 GMT) -- the third-latest start for a US Open night session -- after a four-hour rain suspension earlier in the day.
That delay was compounded when 2009 champion Juan Martin del Potro and Guillermo Garcia-Lopez battled out a four-hour, 13-minute dogfight on the same Arthur Ashe Stadium, which the Argentine sixth seed won 6-7 (5/7), 6-4, 7-6 (9/7).
"I think playing at that time for your first round is not ideal," said Murray, who hit 34 winners against just five unforced errors to book a match with Argentina's Leonardo Mayer for a place in the last 32.
"It's not whether it's me, it's anyone. Just because I won last year, it's nothing to do with that. It's just more for the guys that have to play this evening, and you have guys that have two days off between matches," Murray said.
Amongst Murray's leading rivals for the title, Rafael Nadal completed his first round match on Monday, 48 hours earlier, while top seed Novak Djokovic and five-time winner Roger Federer both wrapped up their openers on Tuesday.
Del Potro and Garcia-Lopez had provided the earlier spice for the Murray headliner when they exchanged angry words over the number of injury timeouts that the Spaniard was taking.
"I just asked about the medical timeout because I didn't know how many or how long. He explained to me then the chair umpire also, and that's it," said Del Potro diplomatically.
Third-seeded Murray, who snapped Britain's 76-year wait for a men's Grand Slam champion when he triumphed in New York last year, needed just 98 minutes to get past 33-year-old Frenchman Michael Llodra, 6-2, 6-4, 6-3.