The Grizzlies closed to within two points with 55 seconds remaining, but could not score again. LaMarcus Aldridge made 1-of-2 free throws for Portland with 2 seconds to go and the Trail Blazers survived a last-second miss by Rudy Gay.
Hickson delivered 19 points and 11 rebounds in helping Portland win for the 10th time in 13 games. The Trail Blazers are 2-1 on a four-game road trip that wraps up Saturday in Minnesota.
Memphis saw its home record slip to 13-4.
Wesley Matthews scored 21 points for Portland and Aldridge had 15 to go with 12 rebounds.