The Frenchman controlled play from the first serve, pushing Murray from side to side and front to back as he mixed in drop shots with backhand drives.
Still, Murray had to find confidence that he can improve, pumping a fist when he played well.
The Scot arrived on centre court to cheers, making a video of the moment as he offered a big smile.
A Scottish flag waved in the crowd.
But the first serve was far from what Murray and the crowd wanted.
A two time winner of the tournament, a nervous Murray double-faulted and was broken in the opening game.
Gasquet, who returned himself in May from groin problems, held to go up 2-0.
Murray then seemed to find himself. The Briton, moving better, won three consecutive games, including a break of serve, to go ahead 3-2.
Gasquet won the next three games to move ahead 5-3 and into position to win the opener.
Murray prolonged the set before Gasquet closed out.
The second set began with Murray once again getting broken, but he played much better.
He had a break point to get back on serve at 2-2. But Gasquet never let go of his early break and eventually went up 4-2.
Earlier Marin Cilic of Croatia became the first seed to fall when the 14th was eliminated by Radu Albot of Moldova 6-4 7-6(6) and Serbia's Miomir Kecmanovic upset Canadian Felix Auger Aliassime 6-3 6-3.
World number two Rafa Nadal, the second seed, withdrew overnight, citing fatigue after winning his fifth Rogers Cup title on Sunday. (Reporting by Gene Cherry in Raleigh, North Carolina Editing by Christian Radnedge)