MEMPHIS, Tenn. — Go ahead and count out the San Antonio Spurs as simply too old to win another title with Tim Duncan, Tony Parker, Manu Ginobili and coach Gregg Popovich.

They’re back anyway with the chance they’ve wanted so very much the past six years.

Parker scored 37 points in his best game this postseason, and the San Antonio Spurs finished off a sweep Monday night of the Memphis Grizzlies with a 93-86 win for their fifth Western Conference title.

“It’s a great feeling,” Parker said as he sat with the Western Conference trophy perched in front of him.

“Since last year, I promised to him (Duncan) that we will go back, go back to the Finals and get an opportunity to win the whole thing and I’m trying to do my best, try to be aggressive every night. I think everybody on the team, we really want to do it for him. We win the West and now it’s one more step. This is the hardest one.”

The Spurs now wait for either Miami or Indiana having swept two of their three opponents already this postseason, this is the first sweep in a conference final since the Nets did it to Detroit in 2003. They also have won six straight in these playoffs, handing two straight losses to a team that had been undefeated on their own court in their best postseason in franchise history.

Memphis finished off its best season ever swept by the very same franchise that needed four games to knock them out of their first playoff appearance back in 2004.

“We will be back,” Grizzlies guard Mike Conley said.

Parker had his best game this postseason as he hit 15 of 21 shots and all six at the free throw line earning the Spurs and Duncan plenty of rest before Game 1 of the Finals on June 6.

“He’s been amazing,” Duncan said of Parker. “Every year he gets better and better and better. He’s been carrying us. You can see tonight he carried us the entire game.”

Duncan hugged Ginobili before heading off the court, celebrating the chance at a title that slipped away a year ago when the Spurs blew a 2-0 lead to Oklahoma City before losing four straight. The 37-year-old Duncan finished with 15 points and eight rebounds. Kawhi Leonard added 11.

“We want to get back there,” Duncan said of making the finals. “We’ve had some really close years where we fell right on the verge of getting back. It feels like forever since we’ve been there.”

Popovich said the fact they are back in the finals after a six-year drought is something he’ll think about once he hits the bed, though he already felt pretty good.

“You don’t expect that to happen maybe this late in the game with the same group,” Popovich said. “It’s tough to do, to maintain something that long. But it just shows the character of those three guys and their ability to play with whoever else is brought in around them. They deserve a lot of credit for that.”

Memphis coach Lionel Hollins had talked about how his Grizzlies needed to dig deep for something they didn’t know they had to take the first step back into this series. But they couldn’t outshoot the Spurs and got beaten once again at their own inside game.

“We just never could gain control of the paint,” Hollins said. “They controlled the paint.”

That the Spurs did as they shot 51.3 percent (39 of 76) from the floor and outscored Memphis 52-32 in the paint, even though the Grizzlies had a 41-34 edge on the boards. Memphis led only briefly and the last at 6-4 as the Spurs took control early.

Memphis stayed close only by getting to the free throw line, making more shots there (17 of 24) than San Antonio took (12 of 13). The Grizzlies also got a career-high 22 points from reserve Quincy Pondexter, 18 of those in the second half. Pondexter was the only player from Memphis to shoot over .500. Zach Randolph finished with 13, continuing his struggles at the line where he was 5 of 8, and Marc Gasol had 14.