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 on Monday night 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 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 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 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.

“We learned that winning isn’t easy and winning championships is one of the hardest things you can possibly do,” Pondexter said. “I think our guys really dug deep to get as far as we did, and San Antonio’s a tremendous team. We’re going to take a couple pages out of their book.”

Duncan had taken care of the Grizzlies scoring the big points in overtime in each of the last two games. Parker took over this time as he hit 14 of his first 18 shots, and he hit the biggest shot with 9:15 left when he knocked down his lone 3-pointer over the outstretched arms of both Tony Allen and Randolph after Memphis gotten within 76-73 with fans sensing the most life out of the Grizzlies all night long.

Parker and Duncan took turns making buckets before Parker got hit in the eye by Gasol’s outstretched hand after missing a shot. When Parker returned with 4:43 left, Gasol went over to him and Parker told him he was fine. Parker then hit a jumper with 4:13 remaining for an 89-81 lead.

“He was outstanding the whole series, and he controlled the series with his penetration,” Hollins said of Parker. “He made shots, made plays. One game he has 18 assists, today he has 37 points. He was huge. But their team played well. You’ve got to give them credit.”

The Grizzlies made one last run and got within three one last time when Gasol scored on a runner in the lane with 48.7 seconds left at 89-86. But Parker hit four free throws in the final 29.7 seconds to seal the victory for San Antonio and its first Western Conference title since the Spurs’ last NBA title in 2007.

The Spurs made it impossible for Memphis to get off to a quick start as they had more points in the paint (16) than the Grizzlies scored in the first quarter as San Antonio went up 24-14 shooting 52.4 percent (11 of 21).

The Spurs cooled off a bit in the second quarter, missing six of seven shots in a stretch. Memphis got into the bonus early, and the Grizzlies used the free throw line to keep San Antonio from doubling up its lead by hitting 8 of 10 at the line. Even Randolph, who has struggled mightily at the line in this series, breathed a sigh of a relief when his first attempt went down, and he knocked down two straight.

The Grizzlies also got a couple 3s from Bayless, the second after Memphis got its best break of the first half when officials called a 5-second call on the Spurs inbounding the ball. Danny Green missed his would-be buzzer beater, leaving the Spurs up just 44-38.

Gasol’s frustration spilled over in the third quarter as he headed to the bench for a timeout when he smacked the press table with both hands. He also went to his knees when officials blew their whistles after he rebounded a miss. But Pondexter, who missed 23 games to a sprained left knee suffered Dec. 29 against Denver, kept the Grizzlies close almost singlehandedly as he scored 12 points in the third.

“We’re going to be better because we played against, to me, one of the greatest teams there’s been in the past 15 years,” Gasol said.

Notes: Parker’s previous best this postseason came in Game 3 when he had 32 points against Golden State in the semifinals. … Teams are now 108-0 when leading a series 3-0. … The Spurs now are 11-1 in closeout games since their last title in 2007. .. The Grizzlies had owner Robert Pera in the stands for only the second home game this season. … The Spurs missed their first eight 3-pointers before Green finally hit in the third quarter.