Parker also dished off nine assists for San Antonio, which stormed back from a 14-point deficit in the fourth quarter.
Tim Duncan added 21 points, seven rebounds and six blocks as the Spurs started their long annual trek while the AT&T Center hosts the San Antonio Rodeo.
The Pelicans got 17 points, 16 rebounds and four blocks from Anthony Davis but fell to the Spurs for a fourth straight meeting.
Notable deaths of 2014 [PHOTOS]
Michael Sam cut from the Dallas Cowboys