The fadeaway shot as the buzzer sounded was the first 3-pointer of the season for Aldridge and nailed down the Blazers' third win in four games.
Aldridge also grabbed 13 rebounds. J.J. Hickson contributed a double-double as well with 26 points and 15 rebounds.
Dallas led 59-44 but the Blazers outscored the Mavericks 32-21 in the third quarter and 32-24 in the fourth to get back into the game.
Nowitzki sank a 3-pointer with 11 seconds left in the game to give Dallas a 104-101 lead. Aldridge came back with 4 seconds to play to tie the score with a 23-foot jumper and then hit the game-winner after a Dallas turnover gave the Blazers another possession.