Playing in just the second Grand Slam quarter-final of his career, 27-year-old Gasquet used his trademark one-handed backhand to near perfection as he closed out Ferrer in three hours and 23 minutes.
"I thought he was a little bit nervous in the wind, so I played on that," said Gasquet.
"I was a little bit tired but the last game was amazing for me. It's wonderful for me to be in the semis. It means a lot."
Gasquet broke the Spaniard, a model of consistency with trips to the quarters or better in the last eight Slams, when he double faulted on break point to seize a 4-2 lead in the fifth set and ended it with a bristling forehand for his 52nd winner.
"He had a bad game at 3-2 for me. I was a little nervous about getting into the semis at the US Open, but I did it. Was a big win for me," he said.
Gasquet will play either second-seed Rafa Nadal or 19th-seeded Tommy Robredo, both of Spain, for a place in Monday's final.