San Antonio held a 16-point lead with five minutes to play and still had to sweat out the win. Utah closed within 107-105 on a 3-pointer by Trey Burke with four seconds to go, but Belinelli then made two free throws to clinch the victory.
The Spurs won their sixth in a row, improving the Western Conference's best record to 31-8.
Parker had 25 points and nine assists while Tim Duncan, Kawhi Leonard and Belinelli all had 15.
Enes Kanter paced Utah with 25 points and 11 rebounds. Alex Burks produced 20 points while Burke had 17 -- 11 of those coming in the fourth period.
San Antonio won its fourth straight home game and its next three will come on its own court. The first of those will be played on Friday against Portland, which has the second-best record in the conference.