Defending champion Novak Djokovic and third-seeded Andy Murray of Britain also advanced.
Fresh off his victory at the Swiss Indoors, where he won his 65th title last week, Federer converted his first break point for a 2-1 lead with a sharp forehand volley and closed out the first set with an ace after losing only three points on his serve.
Story continues below ↓advertisement | your ad hereGasquet saved three break points in the first game of the second set to level at 40-40 but stopped playing after misjudging a shot from Federer that was in, with the Swiss being awarded the point. Gasquet then sent a backhand long and Federer held his serve to move up 2-0.
Federer sealed the win on his first match point to improve his record against Gasquet to 7-1, after losing their first meeting five years ago.
Eighth-seeded Andy Roddick took a big step toward qualifying for the ATP World Tour Finals by beating Jarkko Nieminen 6-1, 6-4.
Roddick never looked in trouble against the Finn and didn't face a single break point as he broke his opponent three times.
Only the top eight players qualify for the ATP Finals in London from Nov. 21-28, with No. 1 Rafael Nadal, Federer, Djokovic, Murray and Robin Soderling having already booked their places.
"Every match I win is significant at this point," Roddick said. "Puts more pressure on the guys behind me. I have a pretty good shot no matter how I do here this week, but I think the last thing you want to do is be in that position where you're at home cheering against somebody hoping that something bad happens to them."
Roddick is in eighth place in the rankings and will be guaranteed a spot at the year-end tournament unless Fernando Verdasco reaches the final in Paris or Jurgen Melzer wins the tournament.
No. 11 Melzer progressed with a 6-3, 7-6 (6) win over Santiago Giraldo.
Roddick, who plays Ernests Gulbis of Latvia in the third round, lost only five of the 29 points played on his first serve.
The former U.S. Open champion, who reached the semifinals twice at the Paris Masters, broke Nieminen immediately to take a 3-0 lead after winning his serve at love.
Roddick then took Nieminen's serve in the sixth game with a crosscourt forehand winner and broke again in the third game of the second set when his opponent sent a backhand wide.
Nieminen saved two match points but Roddick served two consecutive winners to close out the match.
Roddick said he was happy with the speed of the court, which is faster this year and suits his offensive style of play.
"I believe it's become so monotonous as far as what you get. Grass is slow and indoors has turned slow," Roddick said. "So I think it's fair ... They have less time to return. If you actually stick a volley you get rewarded."
Djokovic overcame a slow start and an early break in the first set to beat Juan Monaco of Argentina 6-4, 6-3.
The second-seeded Serb struggled on his first serve but fended off seven of eight break points and took Monaco's serve three times. He'll next play Frenchman Michael Llodra, who beat No. 16 John Isner of the United States 6-3, 6-4.
Murray also had some problems in his 2-6, 6-4, 6-3 victory over former No. 3 David Nalbandian and received treatment for an apparent wrist injury during the decider.
Nalbandian, who missed most of last year because of hip surgery and missed two months this season with a hamstring problem, lost only two points on his first serve in the opening set but tumbled at a crucial point when he was broken in the 10th game of the second set after two consecutive unforced errors, allowing Murray to level.
Murray called for the trainer at 2-2 in the decider and received treatment for about five minutes. He came back on court and quickly recovered, breaking for a 5-3 lead before serving out the match.
"My wrist feels OK just now," Murray said. "I have had a few problems with it in the past, and I felt quite a sharp pain. I'll just have to wait and see if it's still fine tomorrow."
Murray next plays No. 13 Marin Cilic of Croatia, who beat Sergiy Stakhovsky of Ukraine 6-4, 4-6, 6-3.
© 2010 The Associated Press. All rights reserved. This material may not be published, broadcast, rewritten or redistributed.Di Maria clinches Real dealFrederico Gil into second round at Open Sud
