The Trail Blazers lead the first-round series 3-2 entering Game 6 on Friday in Portland.
A basket by Damian Lillard got the Trail Blazers within two points before James Harden stepped back and swished a 3-pointer to make it 103-98 with about three minutes left. The shot brought the crowd, which was clad almost completely in red shirts emblazoned with the words "Clutch City" on them, to its feet.
That started an 8-0 Houston run to close it out. Harden finished with 17 points and seven assists.
Houston finally slowed down LaMarcus Aldridge, limiting him to eight points, after he averaged 35.3 points in the first four games. Wesley Matthews led the Blazers with 27 points and Lillard added 26.
Lin got extended minutes on Wednesday night with Pat Beverley dealing with an illness. Beverley had five points in 21 minutes.
The Rockets led by as many as 17 points in the first half. Portland cut it to one point three times in the fourth quarter, but never went back on top.
Terrence Jones added a basket for Houston after the big 3 by Harden before Howard got after Aldridge on the other end. He blocked his short jump shot, sending it out of bounds. Portland got the ball back and Aldridge got the ball again, but he badly missed a shot with Howard in his face as the shot clock expired, leaving Aldridge yelling for a foul.
The Rockets were up by nine early in the fourth quarter after four quick points from Lin before Portland used an 8-0 run, with the first four points from Nicolas Batum, to cut the lead to 91-90 with 7:39 remaining.
Back-to-back 3-pointers by Matthews cut Houston's lead to 62-58 early in the third quarter. He added 12 more points in the period to finish with 18 of Portland's 29 points.
Howard and Lin carried the Rockets in the third, combining for 18 points. Howard had 10 and Lin scored the rest, including a long two as the shot clock expired with Lillard right in his face.
Matthews, who was 4 for 5 from long range in the third, made two 3-pointers within 20 seconds late in the quarter to cut Houston's lead to two points. But Lin finished off the quarter with a three-point play to make it 82-77 entering the fourth.
Robin Lopez received a flagrant-1 foul when he fouled Howard in the air while fighting for a rebound and pulled him to the ground by the shoulders on the way down. Howard made one of two free throws to stretch Houston's lead to 74-68 with three minutes left in the quarter.
Houston led by three after one and used an 11-0 run to start the second quarter and go up 41-27. Jones scored the first four points in that span and rookie Troy Daniels capped it with a 3-pointer.
The Trail Blazers had six turnovers while the Rockets built the lead and didn't score until a pair of free throws by Aldridge with about nine minutes left until halftime.
Howard picked up his third foul soon after that and went to the bench.
Portland scored the next five points to get within seven but the Rockets used a 10-0 spurt to push the lead to 51-34. Lin had a reverse layup and a 3-pointer during that run.
The Trail Blazers ended the first half with a 14-5 run, with eight points from Lillard, to cut the lead to 56-48 at halftime.
Aldridge had just six points at halftime after sitting out about half of the first quarter after getting his second foul.
NOTES: The Trail Blazers wore patches on their jerseys to honour Hall of Famer Jack Ramsay, who died on Monday at 89. Ramsay coached the team to an NBA title in 1977. The plaid patch has the words "Dr. Jack" and a "77" to honour the championship team. The Blazers will wear the patch for the remainder of the post-season. ... Hall of Famer Hakeem Olajuwon watched from a courtside seat. ... Chandler Parsons added 20 points for Houston.