Shabazz Napier added 16 points, while Noah Vonleh finished with 11 points and 18 rebounds for Portland, which won its second straight and fourth in the last five.
Mario Chalmers led Memphis with 21 points, while Tyreke Evans finished with 20. Marc Gasol had 19 points and 12 rebounds, but was 7 of 20 from the floor, part of the Grizzlies shooting 38 percent for the game, and 27 percent from outside the arc.
The teams were tied at 80 with 6:47 left after Gasol split a pair of free throws. But Jusuf Nurkic, who had 10 points, converted a 3-point play and put the Trail Blazers ahead for good.
Portland controlled the boards 60-35, including 15 on the offensive glass
Portland dominated the game in the first half, but Memphis was able to chip away at the advantage in the third quarter. A 17-7 run pulled the Grizzlies even in the latter stages of the third.
The Trail Blazers were able to retain a 72-71 lead after three.
Portland took the lead to as many as 13 in the second quarter as the Grizzlies continually misfired on their shots. Memphis was 6 of 23 in the quarter as Portland outscored Memphis 32-22 in the frame.
That allowed the Trail Blazers to hold 55-46 lead at the break as McCollum had 16 and Napier had 11.
Evans had 16 for Memphis.
