Aldridge grabbed nine rebounds and C.J. McCollum added 19 points for the Blazers, who pulled away with an 11-0 run in the fourth quarter.
Damian Lillard provided 14 points, five rebounds and four assists.
The Timberwolves, meanwhile, fell while playing without star forward Kevin Love (quad) and starting center Nikola Pekovic (ankle).
Minnesota also learned before the game shooting guard Kevin Martin will be sidelined indefinitely with a broken left thumb.
Ricky Rubio put in a personal-best 25 points and dished off nine assists to lead the T-wolves.
Corey Brewer helped out with 26 points and seven rebounds.