The Spurs outrebounded the Warriors 38-36, forced 14 turnovers and limited them to 16 second-chance points.
"Our energy was good," Parker said. "We got the 50-50 ball; that was huge for us tonight. It was a tough turnaround for us in Game 4. We missed an opportunity at the end and we realize that. Tonight we played for 48 minutes."
Kawhi Leonard added 17 points, Danny Green scored 16 and Tim Duncan had 14 points and 11 rebounds for San Antonio.
Harrison Barnes scored 25 points, Jarrett Jack added 20 and Carl Landry 16 for Golden State, but Stephen Curry was held to nine points.
"I was terrible, plain and simple," Curry said. "They outplayed us as a team. Individually, I didn't have anything on either end. [I was] a step slow, my shot wasn't falling and I was trying to make plays but defensively I lost a little focus."
Parker took advantage, going 9 for 16 and turning the ball over only twice in 34 minutes.
His energy was just as big a spark.
Parker dove over Jack midway through the third quarter to corral a loose ball, rising to lead a fast break that resulted in a dunk by Green.
Even Popovich displayed more energy, chasing referee Ed Malloy down the sidelines from the free throw line to just past midcourt while screaming and motioning for a timeout with 9 minutes left in the game.
The added energy was especially evident against Curry and Klay Thompson.
The Spurs held Mark Jackson's self-proclaimed "greatest shooting backcourt" in NBA history to 6-for-22 shooting.
Spurs 109, Warriors 91
R Tony Parker leads San Antonio with 25 points and 10 assists as the Spurs take a 3-2 series lead.
• Golden State's Stephen Curry finishes with just nine points, going 1 for 7 on 3-pointers.