Aldridge grabbed six rebounds and Wesley Matthews added 18 points with six rebounds in the Blazers' seventh win in nine games.
Robin Lopez contributed 15 points and 10 rebounds.
Kevin Martin poured in 30 points for the Timberwolves, whose three-game winning streak came to an end.
Nikola Pekovic provided 23 points and 11 rebounds.
2014: The Year in Music [PHOTOS]