Troy Murphy scored 14 points for Golden State before leaving in the fourth quarter after taking a forearm in the face from Zach Randolph. Warriors coach Don Nelson said Murphy may have broken his nose and could miss some games.
Randolph led the Blazers with 27 points and 12 rebounds, and Martell Webster had 19 of his 25 points in the first half.
The Warriors led for almost the entire game and were ahead 101-88, but the Blazers went on a 20-7 run to tie it. Portland had a chance to win in regulation but Randolph couldn't get off a jumper before the buzzer with the teams tied at 114.
Davis had a key steal and two free throws in overtime, and the Blazers shot two airballs at the end of the game.
The two teams combined for 73 fouls and Portland committed 24 turnovers.
Rookie Brandon Roy had 19 points and nine rebounds for the Blazers. Jarrett Jack had 16 points.
Davis also had 10 rebounds and six assists. He had 20 points in the first half.
Portland lost 99-89 to Seattle last week in its first preseason game. The Warriors were coming off a 121-115 win over Denver.