Marc Gasol had 15 points and eight rebounds and Courtney Lee scored 12 points for the Grizzlies (23-20), who have won three straight and seven of eight.
Lamarcus Aldridge had 27 points and 16 rebounds as the Blazers (33-13) slipped three games behind Northwest Division-leading Oklahoma City and had their home winning streak snapped at five.
Randolph, the former Blazers forward, registered his 27th double-double of the season as well as his franchise-leading 190th for the Grizzlies, who shot 51.8 percent and led from start to finish.
Portland fell to 18-5 at home.
The Grizzlies, picking up where they had left off in Saturday's 99-81 home win over Houston, shot 58.3 percent in the first quarter against the Blazers and jumped in front 31-22 behind Randolph's 11 points.
Memphis connected four times from 3-point range in the second quarter, including one by Lee that extended the lead to 57-39 with 3:39 to play in the half.
Damian Lillard connected from long range for Portland to start the fourth quarter, sparking a 23-13 run that cut the deficit to 94-81 with 2:27 to play.
NOTES: It was the first of three regular season meetings between Portland and Memphis. The final two games are on March 11 in Memphis and March 30 in Portland.