Gortat is sidelined with a sprained foot and Phoenix, which owns the fourth-worst record in the NBA, decided to rest Dragic despite the fact it had not played since Sunday.
Still, the Jazz needed a big finish to defeat the Suns.
Wesley Johnson scored a season-high 22 points and Kendall Marshall handed out a career-high 13 assists as Phoenix pushed Utah but could not beat the Jazz.
"Well, I thought our young guys fought really hard," said coach Lindsey Hunter, who praised Marshall's work.
The Suns' young point guard, who averages 13 minutes a game this season, played 34 against the Jazz. Along with his assists, he finished with seven points, three rebounds and a steal.
"Kendall did a great job of distributing the ball and running the offense," Hunter said. "I think this is the first time playing extended minutes, so I think it got to him a little bit. He got a little tired."
Phoenix had a difficult time stopping Utah, which made its first six shots at the start of a 34-point first quarter.
"... When they went inside," Johnson said, "our rotations were out of whack."
The Jazz eventually finished shooting 51.8 percent for the game.
Said Luis Scola, who scored 15 of his 20 points in the first half, "We were right there and playing well, but we weren't getting stops consistently. That's a problem. ...
"If you don't get stops, especially in a place like Utah, it's going to be really difficult ... because they have a good team."
Thanks to an 8-0 run at the end of the third quarter, Phoenix trailed 75-71 heading into the fourth.
Phoenix had a chance to get closer, too, but Jermaine O'Neal missed an 18-footer on the Suns' opening possession.
The Jazz responded with a 10-0 run and built a 92-73 lead with 7:11 remaining, sending Phoenix to its eighth loss in nine games.
The Suns dropped to 23-49 this season, with 10 games remaining. They fell out of the playoff race long ago.
Hunter insisted, however, that motivation the rest of the way won't be a problem.
"That's my job," he said. "I don't think it's difficult. As a coach, you have to do what the task calls for. If that is to motivate, that's what I will do. ... I have no problems doing whatever it takes to get guys ready to go."
Hunter also made a promise: "We will continue to fight it out until it's over."