Parker's driving layup put the winners ahead for good at 83-82 with 7:28 left. Parker also had nine assists, two rebounds and two steals.
Roger Mason scored 18 with four rebounds and three assists. Tim Duncan scored 17 with 15 rebounds, while both Michael Finley and Ime Udoka scored 11 points in the Southwest Division-leading Spurs' seventh win in their last 10 outings.
Steve Nash led Phoenix with 23 points and 11 assists. Jason Richardson scored 15 with four rebounds and four steals.
Matt Barnes scored 13 with five assists. Shaquille O'Neal had 14 points with five rebounds, and Grant Hill added 11 points with eight rebounds for the Suns (34-28), who fell 3 1/2 games behind the Dallas Mavericks (38-25) in the battle for the eighth and final playoff spot in the Western Conference.