Gordon Hayward added 14 points off the bench for the Jazz, who have won consecutive games for the first time since Dec. 5 - 12.
Utah was without center Enes Kanter, who sprained his right ankle in a win Wednesday against Minnesota.
Marcin Gortat had 18 points and 11 rebounds for Phoenix. Goran Dragic added 17 points, but only six after the first quarter.
Utah's bench outscored Phoenix's reserves 32-14.
Randy Foye gave the Jazz the lead for good, 47-44, on a 3-pointer with 9:41 left in the third quarter. 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.
The Suns shot 77.8 percent from the floor 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.
Phoenix's nine second-quarter points were a season low for any quarter and just two points off the franchise record for futility.
NOTES: 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. . Phoenix made 14 field goals in the first quarter but only 20 the rest of the way.