Aldridge also grabbed a game-high 16 rebounds and Arron Afflalo added 18 points off the bench for the Blazers, who were coming off a win over the Spurs on Wednesday.
Russell Westbrook continued his hot play of late, recording his third straight triple-double and fifth of the season. He finished with 40 points, 13 rebounds and 11 assists and became the first player since LeBron James in March of 2009 to notch three consecutive triple-doubles.
Mitch McGary scored a career-high 20 points with nine rebounds and Serge Ibaka added 14 points in Oklahoma City's second straight loss.
Nicolas Batum was fouled shooting a 3-pointer and made each of the ensuing free throws to start a a 15-4 run for a 106-103 Portland lead with 3:56 left in the game.
Westbrook then barreled through the lane for a three-point play moments later to tie the game.
The game was still tied with under a minute left when Aldridge split a pair of free throws to push Portland ahead 111-110. Westbrook missed a tough layup at the other end with 33.9 seconds left, but Lillard could not convert his runner as Anthony Morrow pulled in the miss.
Out of a timeout, Westbrook missed another shot from in close and Afflalo converted two free throws to make it a three-point game with 6.3 seconds left.
Wesley Matthews then committed a head-scratching foul on Westbrook, who was grabbed just inside halfcourt shooting a running 3. However, Westbrook front- rimmed the first shot and Lillard knocked down a pair from the line for Portland to account for the final margin.
The Blazers led 28-25 after the first quarter, but Oklahoma City used a dominant second quarter to grab a double-digit lead at the half.
After Chris Kaman opened the second with a basket, Morrow buried a 3-pointer that started a 13-2 run. Westbrook's free throws late in the stanza put the Thunder up 14 and they led 59-47 at the break.
The Blazers used a 7-0 spurt to cut into the deficit out of the locker room, but the Thunder countered with a 10-0 burst to restore a double-digit margin. Portland did not go away, however, as it followed with a 10-0 run of its own to cut Oklahoma City's lead to 69-64 midway through the third. The Thunder managed to take an 89-78 edge into the fourth.
Westbrook became the eighth player in NBA history to average 30 points, eight rebounds and 10 assists in a month ... Aldridge has 29 double-doubles this season ...Oklahoma City outscored the Blazers 21-7 on the fastbreak ... Ibaka, Kaman, Aldridge and Portland coach Terry Stotts all received technical fouls.