The Spurs (35-10) won their fourth straight game and for the eighth time in the last nine games to move a half-game in front of the idle Dallas Mavericks for the best record in the Western Conference.
"That's the least of what we worry about. We've got a lot of things to be concerned with on our own team, and that's how we spend our time," San Antonio coach Gregg Popovich said.
San Antonio made up for some lackluster shooting with tight defense, holding the Jazz to 32 percent shooting.
The Spurs, who began an eight-game road trip, won't play at home again until after the All-Star break.
"We get a lot of our personality as a team on the road and this was a great time for it," said Duncan, who also had eight rebounds.
Bruce Bowen added 13 points, going 3-for-8 on 3-pointers, and Nazr Mohammed ended a late rally by Utah with a block and a three-point play in the final two minutes to help
As poorly as Utah shot -- going 22-for-68 -- the Spurs never led by more than 12. A 10-point lead for the Spurs dwindled to four by the end of the third quarter, but they played just well enough down the stretch to hold off the Jazz.
"We held them to 70 points, so I guess our defense got us through this," Popovich said.
Utah shot poorly from everywhere, including the free-throw line. The Jazz shot 24-of-34 on free throws and also struggled near the basket, missing even on layups.
"Against a team like this you've got to make layups," Jazz coach Jerry Sloan said. "We didn't make them and so that makes it doubly tough because you're not always going to be able to make outside shots.
"Quite frankly, we haven't been a great outside shooting team, but we have been better at layups than what we were tonight."
It was the first of only three meetings between the Jazz and Spurs this season and went the way most of the recent ones have. Until splitting last season, Utah had lost 18 in a row to San Antonio.
The Jazz missed their first seven shots of the third quarter and didn't get a field goal until Collins made a baseline jumper with 6:06 left to cut San Antonio's lead to 47-39.
Matt Harpring, who finished with 12 points off the bench, made a 3-pointer, converted a three-point play after an offensive rebound by Collins and added a 20-foot jumper to get Utah within 59-55 at the end of the third.
Keith McLeod added a 3-pointer as the shot clock was about to expire early in the fourth, and San Antonio's lead was down to 62-58, but the Spurs responded with a 12-4 run.
Duncan made two free throws to start it and added two jumpers, then after a free throw by Mehmet Okur, Bowen answered with a 3-pointer.
"People forget about him and leave him wide open in that corner and he'll punish them for that," Duncan said of Bowen.
Michael Finley completed the run with a free throw on a defensive 3-second violation.
Utah got within 74-67 on a free throw by Collins, who had missed his first of the two attempts with 4:34 remaining, and the Jazz could get no closer.
Okur had a 3-pointer bounce out of the rim on one possession and after stopping the Spurs on defense, the Jazz got the ball down low to Harpring, who was blocked by Mohammed. The Spurs got the loose ball and started a break, which Mohammed finished with a three-point play with 1:51 left in the game.
"We've got a lot of guys who are very confident coming off the bench," Duncan said.
Beno Udrih scored 10 for San Antonio. ... Utah owner Larry Miller announced at the end of the first quarter that the Jazz will retire Karl Malone's No. 32 on March 23 when the Jazz host the Washington Wizards. ... Ostertag received about an even mix of boos and cheers when he entered the game, his first since serving a one-game suspension for an argument with coach Jerry Sloan. ... Nick Van Exel (elbow) and Robert Horry (abdominal strain) were on the inactive list for the Spurs.