Davenport, the second seed, shook off a pulled hamstring and rallied to overcome Amelie Mauresmo of France, 3-6 6-3 6-2, while the third-seeded Williams cruised through the first set before first faltering and then finally rallying for a 6-2, 5-7, 6-4 win over the Spaniard Conchita Martinez.
"She hits a lot of balls back," said Williams after clawing her way to victory in her championships debut. "She was definitely hitting the ball better than she usually does in other matches. I don't know why."
Neither did Martinez, the 1994 Wimbledon champion who has fallen on hard times on the court. But the Spaniard somehow rediscovered her magic and left the athletic Williams frustrated and confused.
"I felt like the old me again," said Martinez, a winner of 34 career singles titles but only one minor tournament this season. "I was hitting my forehand the way I used to and hitting the right shot at the right moment."
In Hartford, Connecticut, the Dutchman Paul Haarhuis began his defence of the ATP Tour world doubles championship without his long-time partner Jacco Eltingh. The difference was evident.
Two-time champions and second seeds Todd Woodbridge and Mark Woodforde of Australia beat the seventh-seeded Haarhuis and the American Jared Palmer 6-4 6-2 in a Green Group round-robin match.
The top-seeded Indian team, Mahesh Bhupathi and Leander Paes, beat eighth seeds Piet Norval of South Africa and Zimbabwe's Kevin Ullyett 7-6, 6-3 in a Gold Group match.
Jim Courier was arrested on a drunken driving charge early yesterday in Orlando, Florida, after running a red light.
Results, Digest, page 31