The score was tied at 82-82 with 8:30 to go when the Rockets embarked on their key surge. Budinger's long-range shot was one of four he hit en route to an 20-point performance.
His final two points came at the foul line with 16 seconds left and gave Houston a seven-point lead.
Houston won its second in a row and improved to 2-1 on a six-game road trip. Portland suffered only its third home loss in 14 games this season.
Portland was led by Jamal Crawford with 21 points.