Third seed Murray was staring down the barrel of defeat after dropping the opening two sets but battled back to dominate the final three and win 5-7, 4-6, 6-1, 6-3, 6-1 as the challenge of world No35 Mannarino wilted.
Murray, who won the US Open in 2012 to claim his first grand slam title, will now face Brazil’s Thomaz Bellucci -- the conqueror of fellow Briton James Ward -- in the next round.
“It was an extremely tough match,” said Murray. “He hits the ball very flat, has fantastic timing, and it is difficult to read where he is going to hit the ball.
“Thankfully in the third set I managed to grab the break point after missing chances in the first two sets. Like I said, it was very tough.”
British No2 Jo Konta, meanwhile, reached the last-32 of a grand slam for the first time in her career by stunning ninth seed and Wimbledon finalist Garbine Muguruza 7-6 (7-4), 6-7 (4-7), 6-2.
The epic showdown, which extended Konta’s winning streak to 15 consecutive matches lasted three hours and 23 minutes, setting a new record for a women’s clash at Flushing Meadows.
Konta will now face Germany’s 18th seed Andrea Petkovic in the third round, while her shock victory over Muguruza has already guaranteed the 24-year-old $120,200 (£78,900) – the biggest pay cheque of their career.
“She’s an incredible fighter and no matter what level she brings, she always brings her top-10 mentality,” said Konta. “I had to fight for every point, it wasn’t given to me.”
Slovenia-born British No2 Aljaz Bedene crashed out of the tournament after losing in four sets to home favourite Donald Young. The 26-year-old claimed the first set but lost 6-3, 4-6, 4-6, 2-6.