The Mavericks appeared to have the game under control early in the third quarter but managed to score only 10 points in the period and wound up having to come from behind just to have a chance in overtime.
Dallas' Shawn Marion hit a layup with 16 seconds left in regulation to forge a 91-91 tie and Jason Terry missed a chance to give the Mavericks the win when he could not hit a 3-point try as time expired.
Marion again tied the score on a layup with 1:42 to go in the extra period and neither side scored after that until Aldridge hit his winning basket.
Dallas fell a game behind Memphis for fifth place in the Western Conference and the defending champion Mavericks began the night with only a 2 1/2-game lead over ninth-place Phoenix in the tight playoff race.
Robert Felton hit 12-of-18 shots from the field and scored 30 points for Portland. Aldridge finished with 25.
Dirk Nowitzki scored 23 for Dallas.
Notable deaths of 2014 [PHOTOS]