Davenport was almost forced into a third set by China's Jie Zheng before claiming the last four games and a 6-2 7-5 victory, while Serena recovered from a wretched start to defeat Russia's Elena Bovina 1-6 6-1 6-4.
Serena struggled from the start and won just one of the first nine points. Then, down 0-3, 0-30, she received a warning for smashing her racket to the ground.
Bovina backed up a solid serve with strong and accurate groundstrokes and broke a second time to run out a comfortable winner of the first set.
Serena finally got going in the second and broke twice to level the match before she raced to a 4-0 lead in the decider.
The former world number one, however, inexplicably allowed Bovina back into the match with some uncharacteristic errors before she closed out the match.
"I think I was trying to kill myself out there," said Serena. "It was really windy and all my shots were out of here.
"I wasn't used to the conditions and...I had to kind of gather myself.
"When I won the second set I was really relaxed and then I just got a little too anxious in the third and was missing a few shots."
Davenport comfortably won the first set on two breaks before allowing Zheng to take a 5-3 lead in the second.
The world number one, however, raised her game, broke with a forehand volley for 4-5 and then again to lead 6-5 when a tiring Zheng netted a forehand.
"I struggled a lot on one side of the court," Davenport said. "The wind was really tricky. I felt I made some errors and rushed some games.
"But I felt like when I concentrated and played more aggressive tennis then I played well.
"It was a good match to play."
In other matches, third seed Anastasia Myskina progressed when French qualifier Marion Bartoli retired with a swollen left knee as the Russian led 4-2.
Spain's Conchita Martinez comfortably defeated seventh seed Nathalie Dechy of France 6-1 6-2, while eighth-seeded Swiss Patty Schnyder beat China's Na Li 6-3 7-6.
Slovakia's Daniela Hantuchova followed up her win over sixth seed Alicia Molik by beating Russian Elena Likhovtseva 7-5 6-4.
