Parker also handed out seven assists and Tim Duncan provided 18 points with nine rebounds as Western Conference-leading San Antonio recorded a fifth straight win and eighth in nine games.
Manu Ginobili netted 14 points in his return from a two-game injury absence (hamstring).
Kawhi Leonard helped out with 13 points with six rebounds.
The Pelicans dropped a sixth straight despite 22 points, 11 rebounds, three steals and two blocks from Anthony Davis.
Brian Roberts contributed 19 points for New Orleans.