Aldridge scored 44 points and took over down the stretch with the game on the line. No other member of the Trail Blazers scored during the last nine minutes.
Portland made up a 13-point deficit in the second half and Denver took its last lead at 105-104 when Randy Foye made a layup with 1:01 to play.
Denver then missed its final four shots while Aldridge was completing his big night by hitting six free throws over the closing 43 seconds.
Wilson Chandler scored 18 points for Denver, which lost its third in a row.
Notable deaths of 2014 [PHOTOS]