Murray triumphed 5-7, 4-6, 6-1, 6-3, 6-1 after his world number 35 opponent had threatened to condemn him to his earliest loss in New York since also making the second round on debut in 2005.
But left-hander Mannarino wilted in the 30-degree heat and humidity in Arthur Ashe Stadium as Murray's greater freshness and physical condition proved crucial.
Murray goes on to face Brazilian 30th seed Thomaz Bellucci for a place in the last 16.
"I was leaving the ball too short and he made me do a lot of running."
Murray, who had needed four sets to beat Nick Kyrgios in the opening round, fired 21 aces -- the last of which was on match point -- while Mannarino was undone by 61 unforced errors.
It was a familiar tale of woe for the 27-year-old Frenchman, who also had a two sets to love lead over Feliciano Lopez at the Australian Open in January before retiring with heat exhaustion in the fourth set.
