Portland's winning streak was tied for the second-longest in franchise history. The team also won 13 consecutive games in 2007.
Chris Paul added 22 points for the Rockets, who have won six straight and 23 of their last 24 and have the best record in the NBA.
Al-Farouq Aminu had 22 points, including six 3-pointers, for Portland. The Blazers had also won nine straight at the Moda Center.
Harden and Trevor Ariza each hit 3-pointers to stretch Houston's lead to 110-102. Harden added another 3-pointer with 1:55 left and it seemed Portland was out of it.
But the Blazers rallied with a 9-0 run, capped by CJ McCollum's floater with 28 seconds left to pull within 113-111.
Paul went to the line with 1.3 seconds left and made both shots. After a timeout, Lillard tried a 3-pointer but it missed.
Jusuf Nurkic finished with 21 points and 11 rebounds for Portland, while Lillard had 20 points. Neither Lillard nor backcourt mate McCollum hit a 3-pointer in the game.
Aminu had four 3-pointers in the opening quarter and finished with 16 points to lead all scorers. Harden had 14 for the Rockets, who trailed 31-27 going into the second.
Evan Turner put back his own layup to cap an 11-2 Portland run and put the Blazers up 42-38. Turner had to leave the game later in the period after he sustained a cut that appeared above his left eve.
Harden was booed each time he had the ball by the Moda Center crowd, but he finished the half with 21 points and the score was knotted at 55.
Portland had five 3-pointers in the first quarter compared to Houston's one - but the Rockets' production picked up in the second quarter with seven 3s. The Rockets went into the game with the league's best 3-point percentage at 50 percent, while the Blazers were next at 45.5 percent.
Houston finished with 19 3-pointers while Portland had 11.
Portland was hurt when Nurkic got his fourth foul with 4:08 left in the third and went to the bench with 15 points and 10 rebounds. Paul's 3 gave the Rockets an 86-85 lead just before the third quarter ended.
Houston has won all three meetings this season.
Rockets: It was the last game on Houston's three-game road trip. ... Harden scored the first nine points in the first half, and the first nine points in the second half.
Trail Blazers: Lillard is still awaiting the birth of his first child. His girlfriend's due date was Monday. ... Former Oregon running back LaMichael James was at the game, as was former Portland center Chris Kaman.
Rockets: Host Detroit on Thursday.
Trail Blazers: Host the Boston Celtics on Friday.