Fourth-seeded Cypriot Marcos Baghdatis lost 1-6, 7-6, 6-2 to Austrian left-hander Stefan Koubek while eighth-seeded Serb Novak Djokovic was beaten 6-3, 6-3 by Stanislas Wawrinka of Switzerland.
Argentine David Nalbandian, seeded second, eased through with a 6-2, 6-3 triumph over Austria's Oliver Marach.
In a match of the highest quality, Roddick struggled to deal with the powerful groundstrokes and fierce backhand passes of Gasquet, one of only four players to beat world number one Roger Federer in the last two seasons.
The first-set tiebreak ended in controversy when a spectator called out during a Roddick second serve at 5-5, the American netting a forehand before Gasquet took the set.
"It was a little annoying," Roddick told reporters. "I don't feel I got much on the second serve because I hesitated halfway through it."
An angry Roddick knocked over a bin at courtside and remonstrated with the umpire to no avail.
LESS DEPTH
"Sometimes
"But I think it was all in jest. He was smiling at the end of it."
Gasquet had less depth on his groundstrokes in the second set as Roddick bounced back.
The American also served well, giving up only three points on serve in the second set and two in the third.
A break at 4-1 allowed Roddick to serve out the second set to love, and further breaks at each end of the third set secured a satisfying victory.
"I came out of the first set thinking this is trouble because I felt like I hit the ball pretty well and still got on the bad end of it," said Roddick.
"He was able to hit some shots that not a lot of people can."
Baghdatis said he felt jaded during his defeat by the unseeded Koubek.
"I think I'm a bit tired. Mentally I'm not ready," said the Cypriot.
"On the important points I just wasn't there and I couldn't finish the match off."