Portland dominated the fourth quarter to win its third in a row and improve its home record to 16-4.
Aldridge produced 32 points and 18 rebounds, the second time in three games he has reached the 30-point mark. He came into the game as the NBA's sixth leading scorer.
Lillard had five assists to go with his six rebounds and 28 points. Luol Deng led Cleveland with 25 points and Kyrie Irving had 21.
The Cavaliers remained stuck on four road victories this season, tied for second fewest in the NBA.