Damian Lillard prevented the series from going back to Houston with his 3-pointer as time ran out. He finished with 25 points.
The shot gave Portland a 99-98 victory in Game 6 on Friday night and propelled the Blazers to the Western Conference semifinals for the first time in 14 years.
Portland, making its first playoff appearance since 2011, had been eliminated in the first round in its last six trips, and hadn't advanced to the second round since 2000.
LaMarcus Aldridge led the Blazers with 30 points and 13 rebounds. James Harden led the Rockets on Friday night with 34 points. Dwight Howard had 26 points and 11 rebounds as Houston failed to become the ninth team to come back from a 3-1 deficit in a best-of-seven playoff series and advance.