Rudy Gay's jumper from near the top of the key was off the mark, allowing the Trail Blazers to escape a closely played game that saw nine ties and 21 lead changes.
Marreese Speights had a season-high 22 points and 13 rebounds for the Grizzlies in place of Zach Randolph, who missed the game with flu-like symptoms. Gay had 19 points, but was 8 of 21 from the field.
Randolph, the Grizzlies' leading rebounder and second-leading scorer, missed his first game of the season.
The teams were tied at 80 with 4:05 left, the ninth tie of the game, when Hickson hit one of two free throws. Batum's 3-pointer with 3:28 remaining put Portland, which never led by more than four, ahead for good.
Memphis was within 85-84, but Mike Conley missed a layup with 7.9 seconds left, and the Trail Blazers were able to secure possession and the victory as Aldridge split a pair of free throws with 2.1 seconds to go.
Memphis carried a 50-47 lead into halftime behind 17 points from Gay, who was 7 of 13 from the field. Gasol had eight points, but already had surpassed his career best with seven blocks in the half.
Hickson and Matthews led the Trail Blazers with 10 points apiece.
Memphis had the lead to eight points in the half, but could never extend it to double digits as Batum, Hickson and Matthews were a combined 11 of 18 from the field.
The Grizzlies missed eight of their first nine shots in the game, but finished the half shooting 51 per cent, while Portland was at 46 per cent.
Speights picked up the offensive pace for Memphis in the third quarter, scoring 16 of the Grizzlies' first 20 points.
But Portland was getting its offensive production from several sources. Matthews connected on a trio of 3-pointers, while Hickson and Aldridge helped with the scoring. That helped the Trail Blazers tie it at 72 at the end of the third.
NOTES: Memphis G Jerryd Bayless returned after leaving Wednesday's game at Boston with a left ankle sprain. .The Trail Blazers, whose bench averages only 17.7 points a game, the worst in the league, contributed only nine points against Memphis. . Aldridge made five free throws in the game, putting him past Kevin Duckworth for 10th place on franchise list in that category. . Gasol's previous career high was six blocks at Phoenix on Dec. 12. .Former Memphis Tiger Will Barton got a nice round of applause when he entered the game for Portland. He ended night with four points.