San Antonio Spurs' Tony Parker (9) passes to teammate Tim Duncan (R) between Memphis Grizzlies' Marc Gasol (L) and Tony Allen during Game 4 of their NBA Western Conference final playoff basketball series in Memphis, Tennessee, May 27, 2013. [Photo/Agencies]

MEMPHIS, Tennessee - Written off by many as too old to contend anymore, the San Antonio Spurs booked a place in the NBA finals by completing a sweep of the Memphis Grizzlies on Monday.

Tony Parker scored 37 points in his best game this postseason as San Antonio beat the Grizzlies 93-86 to complete a 4-0 win in the Western Conference series and reach the finals for the first time in six years.

"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 Tim (Duncan) we would go back to the finals and get an opportunity to win the whole thing. Everybody on the team, we really want to do it for him. We win the West and now one more step. It's the hardest one."

San Antonio Spurs owner Peter Holt (R) celebrates with Tony Parker after the Spurs eliminated the Memphis Grizzlies to win the NBA Western Conference final playoff basketball series in Memphis, Tennessee, May 27, 2013. [Photo/Agencies]

The Spurs now 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.

Parker 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 Manu 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 by 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."