"We kept attacking and didn't settle for too many outside shots," Jefferson said. "We kept attacking the paint."
The Jazz were dominant down low, hitting 30 of 58 shots in the paint for a 60-28 advantage.
"That's how we've got to play," Millsap said. "We come out and put it all on the floor and good things are going to happen."
Not including Utah's six free throws, the Jazz scored only 18 points outside the key.
"Almost everything they did was in the paint except a couple of jump shots," Suns coach Alvin Gentry said. "That's the toughest thing."
Gordon Hayward added 14 points off the bench for the Jazz, who have won consecutive games for the first time since they won four in a row Dec. 5-12.
"I didn't like the first quarter but after the first quarter until the last three minutes of the game I thought we picked it up on the defensive end."
Utah's bench outscored Phoenix's reserves 32-14 and scored 25 points off a season-high 21 Suns turnovers.
"They weren't forced," Gentry said of the turnovers. "We threw it away."
Utah was without center Enes Kanter, who sprained his right ankle in a win Wednesday against Minnesota.
Randy Foye gave the Jazz the lead for good, 47-44, on a 3-pointer with 9:41 left in the third quarter -- Utah's only 3-pointer on nine attempts. Four minutes later, Jefferson scored six straight points to key a 14-2 run that stretched Utah's lead to 65-52.
Phoenix pulled no closer than seven the rest of the way, needing a 10-0 run in the final two minutes to narrow the final margin.
The Suns shot 77.8 percent in the first quarter to take a 31-25 lead, with three of four starters scoring eight points or more.
But that abruptly changed in the second quarter, when the Suns' second unit went 8:24 without scoring. Fortunately for Phoenix, the Jazz were just as cold -- the teams combined to miss 21 consecutive shots over a 4:28 span and Utah led only 42-40 at halftime.
"I don't know what happened," Dragic said. "The second unit didn't move the ball as well. They were playing more one and five and taking tough shots. When you play like that you're not getting good looks, you're shooting over hands and you shoot a low percentage."
Phoenix's nine second-quarter points were a season low for any quarter and just two points off the franchise record for futility.
"I thought the first quarter was the best we've played all season," Gentry said. "But the last three quarters were as bad as possibly could have played."
The Jazz had not won in Phoenix since March 4, 2010. ... Utah won on the road for the first time since Dec. 23. ... The Suns scored seven points in a quarter on Nov. 11, 2006, against Memphis. ... Millsap missed the final nine minutes of the first quarter after he bumped heads with Suns forward P.J. Tucker. Millsap needed three stitches in his right earlobe but returned at the start of the second. Later in the game, he took a shot to the throat. ... Phoenix made 14 field goals in the first quarter but only 20 the rest of the way. . Suns guard Jared Dudley, known locally for his lack of dunking ability, was fouled on a dunk for a "dunk and one," his first, he said, since college.