Douglas finished with 11 points, scoring the game's final six points to seal Memphis' fifth straight victory.
Gasol was 13 of 24 from the field, including 4 of 6 from outside the arc. But Douglas, signed by Memphis this week because of injuries, took over down the stretch. The guard scored on a 19-footer with 34 seconds left, then converted two pairs of free throws in the last 20 seconds.
CJ McCollum led the Trail Blazers with 24 points, and Damian Lillard had 19 on 6-of-18 shooting. Evan Turner had 15 points and 10 rebounds.
