Damian Lillard scored a game-high 32 points and handed out seven assists for Portland. He was 4-for-8 from 3-point range and 12-for-13 from the free throw line.
LaMarcus Aldridge scored 19 points and grabbed 10 rebounds, but was just 8- for-23 from the field and Nicolas Batum chipped in with 15 points and eight rebounds for the Trail Blazers, losers in three straight and four of their last five.
"I'm just missing shots," Aldridge admitted. "I have had great looks and I've missed them. I am going to find my rhythm and I am going to make those shots that I've been missing soon."
Portland shot just 40.7 percent (35-for-86) from the field.
Batum knocked down an open 3-pointer just over five minutes into the game to give the Blazers a 10-6 lead. The Grizzlies battled back and took an 18-17 lead, but Portland regained the advantage and led 23-20 with 14.4 seconds left. Gasol, though, knocked down a buzzer-beater to cut the Memphis deficit to 23-22 entering the second quarter.
After Thomas Robinson tied the game at 31-31 early in the second quarter, Memphis opened up a 13-5 swing to take a 44-36 lead with just over 4 1/2 minutes remaining in the first half.
The Grizzlies' lead swelled to 12 after Conley hit a 3-pointer with just under a minute remaining, but a Lillard triple and Aldridge's layup in the closing seconds made it 54-47 entering the break.
Memphis opened up the third on an 11-3 run to take a 65-50 lead and didn't see its spread dip below double digits until Lillard hit a step-back jumper with one second left in the third to pull the Blazers within 78-69.
"It was big for us to be able to play from the lead and just kind of keep holding them off," Memphis head coach David Joerger said.
Portland never got closer than nine the rest of the way.