The Trail Blazers ended the Thunder's winning streak at eight games and boosted the best record in the Western Conference to 16-3.
LaMarcus Aldridge scored 38 points and grabbed 13 rebounds to fuel the Portland win. The Trail Blazers also have victories this year over San Antonio and Indiana to confirm their position as the surprise team of the NBA.
Russell Westbrook brought Oklahoma City to within a point on a layup with 1:44 to play and neither team could score again until Batum hit his key shot. After Kevin Durant missed a 3-point try for the Thunder, Aldridge hit two free throws to secure the victory.
Aldridge hit 17-of-28 shots from the field while Batum and Damian Lillard both had 14 points.
Durant led Oklahoma City with 33 points. The Thunder led by 11 at halftime, but gave up that advantage while being outscored 35-21 in the third period.
Portland is off to the second-best start in franchise history through 19 games.