Lowry also had nine assists and grabbed eight rebounds. Martin was true on four consecutive free throws in overtime that wrapped up the victory.
Houston improved to 4-1 at home this season.
The Trail Blazers were hobbled by the loss of top rebounder Marcus Camby, who missed the game with a sprained left ankle.
Portland got 29 points, eight rebounds and four blocks from Nicolas Batum in its third straight loss.