The Warriors held Stephen Curry out of the second half as a precaution after another player rolled up on his surgically repaired right ankle late in the second quarter.
Sasha Pavlovic hit a 3-pointer with one minute left to pull the Blazers within 96-95. Klay Thompson made one of two free throws for the Warriors before Pavlovic missed another 3 with 40 seconds to go.
Former Blazer Jarrett Jack hit a layup to extend Golden State's lead to 99-95 with 19 seconds left. Will Barton's basket on the other end kept the Blazers in it, but it was as close as they would come and Thompson made free throws for the final margin.
Klay Thompson had 19 points and Carl Landry had 18 for the Warriors (5-1), who trailed by as many as 12 points in the first half.
LaMarcus Aldridge had 18 points for the Blazers (2-3).
Rush made a pair of free throws to even it at 30, and he added a hook shot to put Golden State ahead 37-34.
Curry went to the end of Golden State's bench after hurting his ankle, but moments later appealed to coach Mark Jackson to go back in. Jackson said no and Curry headed for the locker room.
The team said at halftime that Jackson was sitting Curry for the rest of the night as a precaution.
Curry had surgery on the same ankle in April. He missed 40 games last season because of trouble with the ankle, and averaged career lows of 14.7 points, 5.3 assists and 3.4 rebounds.
The Blazers pulled within 51-48 at the half and the two team kept it close throughout the third quarter. Harrison Barnes put Golden State in front 70-68 with a 3-pointer, but Batum answered with his own 3.
The Warriors led 81-76 going into the fourth quarter after Richard Jefferson's jumper. They upped the lead to 90-83 with 6:30 left on Thompson's driving layup.
The Blazers saw the return of top draft pick Damian Lillard, who missed a game with a bruised left foot. Proclaimed the team's franchise point guard by general manager Neil Olshey, Lillard was the sixth overall pick in the June draft out of Weber State.
Lillard said he was anxious to make his Rose Garden debut against Golden State, because he grew up in Oakland. He went into the game averaging 16.3 points, which led all NBA rookies. He finished the night with 15 points.