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.
Gasquet saved three break points in the first game of the second set to even at 40-all 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.
"I don't think there was much between us except that I made a couple of games where I played really well, in which I was able to make the difference," Federer said. "I have more experience, I know how to play the key points."
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 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."
Djokovic overcame a slow start and an early break in the first set to beat Juan Monaco of Argentina 6-4, 6-3, while Soderling needed just 63 minutes and 11 aces to down Frenchman Gilles Simon 6-4, 6-0.
Djokovic struggled on his first serve but fended off seven of eight break points and took Monaco's serve three times. The second-seeded Serb next plays 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 even it.
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."