Aldridge finished with 26 points and 13 rebounds, Matthews contributed 24 and Damian Lillard added 21 points, eight assists and five rebounds.
Manu Ginobili led all scorers with 29 points, but no other Spur scored more than 14. San Antonio shot 40 percent from the floor and 33.3 percent from three in the final quarter and couldn't string together enough consecutive defensive stops to stay in the game.
The Blazers, not known for their defense, held San Antonio, the league's third-best offense, to 44.2 percent shooting and 2-of-7 from behind the arc in the first half. Boris Diaw dropped in a floater at the last second, bringing the score to 54-49 in Portland's favor heading into halftime.
Spurs coach Gregg Popovich was thrown out of the game early in the third quarter for relentlessly screaming at an official. No, seriously:
Ginobili responded to his distressed coach's outburst, scoring 18 points in six minutes of playing time in the third quarter and giving San Antonio a 78-77 lead heading into the final quarter.
The fourth quarter, however, belonged to Aldridge. The All-Star forward took control, scoring six points down the stretch. The Spurs decided to double with just over a minute remaining and Aldridge kicked the ball out to the perimeter. The ball found Matthews, who drained a three to give Portland a nine-point, 105-96, lead. The Blazers didn't look back from there.