San Antonio had a chance to sweep on Monday night, but Portland pulled out a 103-92 victory.
With their backs against the wall, Portland was led by its point guard. Damian Lillard scored 25 points and was one of five Trail Blazers in double figures for the night.
"We knew that this could have been our last game if we didn't come out and correct the things that we had been doing wrong over the first three games," said Lillard. "I think guys were locked in. Everybody competed."
Lillard was 11-for-21 from the field on Monday after shooting 37.5 percent over the first three games.
LaMarcus Aldridge was next for Portland with 19 points, followed by a sensational all-around effort from Nicolas Batum, who had 14 points, 14 rebounds and eight assists.
Wesley Matthews added 10 and Will Barton gave the Blazers bench a much-needed lift with 17 points.
"It was a good game, but we still got another three to go," Blazers head coach Terry Stotts said.
Tony Parker was held to 14 points after going for at least 29 in three of his last four games. Tim Duncan had 12 points and nine rebounds for San Antonio, which is looking to head to the conference finals for a third consecutive season.
Boris Diaw (12), Kawhi Leonard (11) and Patty Mills (10) also scored in double figures for San Antonio.
"I don't think that we had the energy, the focus," said Spurs coach Gregg Popovich. "We didn't accomplish our defensive tasks the way we had the first three games. Both mentally and physically, we played at a lower level than we have."
After leading for just 33 seconds over the first three games, Portland used a big run during the middle stages of the third quarter to pull away in this one. The Blazers led throughout the second half, building a 20-point, fourth- quarter cushion.
No NBA team has ever lost a best-of-seven playoff series after going up 3-0. The Blazers were the last team to take one to a seventh game, but lost to the Dallas Mavericks in a 2003 first-round series.
"Like we said, why not us?," asked Batum. "It's never been done before. We're down 3-0. We know it's going to be tough. It won't be easy, especially against this team, the San Antonio Spurs. Like we always say, just take one game at a time.
"We had a great game tonight. We'll try to do the same thing, go down there to San Antonio and just be focused on that game and move on."
A potential Game 6 would be Friday night in Portland.