After San Antonio took its biggest lead at 84-63, the Suns scored eight in a row to cut it to 84-71 on Gortat's three-point play with 6:42 to go. But Green made another 3 and it was 87-71 with 6½ minutes remaining. The final 10-point margin was as close as it got after that.
Gortat scored 16 in the first half on 8-of-12 shooting but no other Phoenix player had more than four in the first two quarters.
Mills had 12 points and Splitter 11 to lead first-half scoring for San Antonio.
Parker probably shouldn't have played in Friday night's overtime loss to Golden State, Popovich said, and there was no doubt he would sit this one out at the end of such a long trip and facing the worst team in the Western Conference.
"We're asking everybody to step up and pick up the slack again," Duncan said. "Tony has been our best player all year long and our most consistent player all year long. He's got a little injury so it's great to give him some time off and let him get healed. It was just great to get a win for him."
The Spurs play their next six at home, starting with a rematch against Phoenix on Wednesday night.
Notes: The Spurs' long road trip, which was separated by the All-Star break, is an annual affair due to the San Antonio Stock Show and Rodeo. ... San Antonio last played at home Feb. 2 against Washington. ... Phoenix has lost three straight at home by 28 to Oklahoma City, 30 to Boston and 11 to San Antonio. ... Suns G Shannon Brown sat for the fourth straight game by coach's decision. ... Markieff Morris, in his second game since being reunited with twin brother Marcus, fouled out in 18 minutes on the court.