Roddick, coming off a win last week in San Jose, beat Fish for the sixth straight time to set up a match Friday against eighth-seeded Robin Soderling.
"A lot of it depends on how he serves," Roddick said. "He can serve great at times, and when he has, it's been very, very tough. ... I think I've gotten the lucky breaks in the matches against Mardy."
Roddick, the 2002 champion, had 14 aces and only lost seven points on serve in the match, three of those points coming in the second game of the second set.
"I think I could have lost that game, and I don't know if it would have affected me much from the standpoint of how I was hitting the ball," Roddick said. "Maybe it took a little bit of the wind out of his sails."
Soderling beat Romania's Victor Hanescu 6-2, 6-1. The Swede is coming off a runner-up finish in Rotterdam on Sunday.
"Soderling's been playing very well, and he's crushing guys here so far," Roddick said. "If I had to choose, the two of us are probably playing the best of anyone in the tournament right now."
In other second-round matches, Sweden's Jonas Bjorkman beat fifth-seeded Sam Querrey 6-4, 4-6, 7-6 (4); Australia's Chris Guccione edged sixth-seeded Thomas Johansson of Sweden 6-3, 6-4; and Donald Young beat Colombia's Alejandro Falla 6-1, 1-6, 6-3.
"When I'm playing well, I'm hitting the ball hard, making the person run," Davenport said. "I felt like I was in control of most of the points, and that's how I'm going to be the most successful."
With Davenport leading 2-1 in the second set, the match was stopped for trainers to work on Wozniacki's abdomen. Wozniacki won only nine points off Davenport's serve.
"I know she is a good, up-and-coming player, so it was important for me to get off to a good start, which I was able to do," said Davenport, back at full strength after giving birth to her first child in June. "I felt like I would be able to overpower her, and I was successful doing that and managed to keep the momentum all the way through."
Davenport will face New Zealand's Marina Erakovic, a 4-6, 6-3, 6-3 winner over Russia's Alia Kudryavtseva. In the other quarterfinals, third-seeded Shahar Peer of Israel beat seventh-seeded Sofia Arvidsson of Sweden 3-6, 6-1, 6-3 and fifth-seeded Olga Govortsova of Belarus edged Germany's Julia Goerges 7-6 (5), 6-2.