The U.S. and International teams each won three four-ball matches at Harding Park in San Francisco, setting the score at 6 1/2 to 5 1/2 at the halfway mark.
"I don't think there's anything wrong with leaving here 3-3," Fred Couples, the American captain, said after the day's split. "We have to come out and fight tomorrow."
"Steve and I gel well together," Woods said. "In this format, you have to make a bunch of birdies. We did most of the day."
Americans Phil Mickelson and Justin Leonard scored a 3-and-2 win over Retief Goosen and Adam Scott and the U.S. team of Zach Johnson and Hunter Mahan beat Robert Allenby and Camilo Villegas 2-and-1.
For the Internationals, Ernie Els and Mike Weir topped Jim Furyk and Anthony Kim 2-up, Y.E. Yang and Ishikawa downed Sean O'Hair and Kenny Perry 4-and-3 and Tim Clark, teamed with Vijay Singh, sank a 15-foot eagle putt on the final hole to give them a 1-up victory over Stewart Cink and Lucas Glover.
"I was pretty calm until I had to stand over it," Clark said.