The Spurs started fast and finished strong as they seized the Western Conference Finals with a 4-0 best-of-seven triumph that put them back in the NBA finals for the first time since 2007.
Parker was sensational in making 15 of his 21 field goal attempts and Tim Duncan added 15 and eight rebounds in the clinching game.
San Antonio has earned an extended rest period as they now await the winner between Miami and Indiana in the East for a championship match-up that does not begin until June 6.
Having squandered a 2-0 series lead in last season's West finals, San Antonio were determined to finish the job this time around.
The veteran squad took a 24-14 lead after the first quarter and did not blink when the Grizzlies made a late push.
Memphis, playing in their first ever conference finals, played from behind most of the night but pulled to within 76-73 early in the fourth quarter.
Parker responded with a three-pointer, Duncan added a quick dunk to push the advantage back to eight and San Antonio were on their way.
Reserve Quincy Pondexter led the Grizzlies with 22 points, Marc Gasol had 14 and Zach Randolph added 13.
Memphis had gone undefeated at home through the first two play-off series before being beaten twice by the Spurs to end their season.