Memphis had been the franchise best known for empty seats and the unenviable NBA mark for playoff futility at 0-12 after being swept in its first three appearances. This time, a third straight sellout crowd cheered every bucket with a couple signs begging the Grizzlies to "Finish Them" in a town in desperate need of a hero.
The Grizzlies needed 10 seasons, but they have become just that as only the second No. 8 seed to upset a No. 1 seed since the NBA expanded the opening series to a best-of-seven.
They will play Oklahoma City in the semifinals.
Marc Gasol had 12 points and 13 rebounds for Memphis. Tony Allen added 11 points, and rookie Greivis Vasquez had 11 off the bench playing 24 minutes with Mike Conley in foul trouble most of the game.
Tony Parker led San Antonio with 23 points, Manu Ginobili had 16, Tim Duncan 12 and Antonio McDyess 10.
The Spurs led only twice at 2-0 and again at 80-79 when McDyess hit a 15-footer with 4:41 left.
That's when Randolph, the man cast off and unwanted when he arrived in Memphis in the summer of 2009, took over and scored 17 of the Grizzlies' 29 points in the fourth quarter.
He scored 10 of the next 14 for Memphis, with his hook putting Memphis ahead to stay at 81-80. Conley added a jumper, then Randolph hit a fallaway jumper, two free throws and another fallaway jumper for an 89-82 lead with 1:55 left. Randolph went to the bench to a huge cheer with 3.4 seconds left.
The Spurs, winners of 61 games in the regular season and the dynasty with four NBA titles with Duncan, turned the ball over three straight times while Randolph was putting away this franchise's biggest win. One desperate pass from Ginobili went right off Parker's hands.
San Antonio had gotten a reprieve with Gary Neal's clutch 3 getting the Spurs to overtime as they staved off elimination Wednesday night. But the Spurs talked of how lucky they were to pull out a game when they had their bags packed for the offseason.
Ginobili also had a big shot to help the Spurs stay alive. This game, he had an even more amazing shot, beating the buzzer at the end of the third quarter as he tossed up the ball from half court off balance and trying to beat the clock. He had been 3 of 10 from the floor before that lucky attempt pulled the Spurs to 70-66.
It just wasn't enough for a team that couldn't beat the Grizzlies in Memphis during the regular season and or the postseason. The Spurs edned this season dropping nine of the last 10 on the road and 16 of the last 19 in the postseason away from San Antonio.
Parker opened the game with a pair of free throws, then the Grizzlies took over. Allen scored on a floater in the lane, Randolph tipped in the ball as the start of 10 straight points by the Grizzlies. That prompted Spurs coach Gregg Popovich to scream at a referee for a timeout. But Vasquez and Allen scored for a 14-0 spurt before Parker finally answered with a layup.
For Memphis, it was almost as dominant as the third quarter of Game 4 when the Grizzlies outscored the Spurs 30-15. This time, the Spurs didn't score from the floor for the first five minutes as the Grizzlies opened with a 28-16 lead after the first 12 minutes and led by as much as 14. The Spurs had six turnovers in the period.
Duncan, who turned 35 on Monday, looked every bit of those years early as he almost stumbled trying to drive to the basket. He later added an emphatic dunk that pulled the Spurs within 46-43 at halftime.
NOTES: Memphis had only 44 points in the paint in the series until Friday night. The Grizzlies outscored San Antonio 62-36 in the paint.