"We were a little flat," coach Tyrone Corbin said. "But we toughed it out when we needed to."
Paul Millsap scored 18 points for Utah, including two on a thunderous rebound dunk with 43.6 seconds left that gave the Jazz an 88-82 lead.
Millsap, still recovering from a bout with the stomach flu, saw Al Jefferson's 17-footer bounce off the rim and soared for the critical putback despite a diminishing energy level.
"I jumped higher than I expected to," he said. "I felt like I wasn't going to make it at first. But I got there."
According to Millsap, the Jazz were motivated by San Antonio coach Gregg Popovich's decision to play them without Duncan, Parker and Ginobili.
None of Spurs' Big Three even made the trip after their 114-104 win over Utah on Monday night in the first game of this home-and-home series.
"It's kind of a slap in our face that they aren't playing three of their top guys," Millsap said. "We recognized it and I think that was the motivation that got us over the hump. That got us through, just thinking about that."
The game was like a trip to the dentist for the Jazz, who struggled and squirmed and found themselves trailing, 75-67, with 8:48 remaining.
Jamaal Tinsley's critical jumper ignited Utah, which used a 21-7 run to overtake San Antonio.
The Spurs converted only three of 15 possessions during the stretch that kept the Jazz's playoff hopes alive.
"Aggressive defense," Corbin said. "I mean, we took our defense up to another level. We got aggressive with our hands. The guys on the ball were aggressive and closed out. They got some 3-point shots, but they were contested shots."
Gordon Hayward re-entered the game with 7:02 left and seemed to trigger the defensive intensity.
"We were more active," he said. "We made passes difficult. They are a good team. They run their offense pretty well. They make sharp cuts and sharp passes. So they are hard to defend. But I think we were a little more active toward the end."
Offensively, Harris provided the boost that Jefferson was unable to do against the Spurs, who fronted him throughout the game and limited him to only 12 shots.
"Just doing my part," Harris said. "I thought they did a great job of fronting Al all night look. We weren't able to get him clean looks in the post. He's our go-to guy. So [I] just took some shots and obviously was able to make them."
Including a pair of 3-pointers, Harris' scoring took the Jazz from a 75-73 deficit to an 84-80 lead. After a basket by the Spurs' Tiago Splitter with 1:45 left, Millsap's rebound dunk sealed the victory.
"A little fatigue set it, but we found a way to win the game," Millsap said. "That's all that matters.
"Big Al couldn't get too many touches down there so somebody had to do it and Devin did a great job of opening it up for us."
Storylines Devin Harris comes to the rescue
R IN SHORT • Devin Harris scores 11 of his 25 points in a three-minute stretch of the fourth quarter as the Jazz beat San Antonio.
Key Moment • When Spurs coach Gregg Popovich decides to leave home stars Tim Duncan, Tony Parker and Manu Ginobili to rest.
Key Stat • Paul Millsap finishes with 18 points, including the clinching dunk that makes it 88-82 with 43.6 seconds remaining.