Michael Beasley's follow dunk after a Jazz turnover cut Utah's lead to 79-74 with about 5 minutes remaining.
But Jefferson's steal and 19-footer by Paul Millsap halted a nearly 6-minute scoreless streak for the Jazz and started a 7-0 run, capped by Marvin Williams' 3 pointer.
Millsap added 18 points and 13 rebounds for Utah.
Luis Scola led the Suns with 21 points and Jared Dudley scored 16.
Jamaal Tinsley went scoreless starting in place of injured Mo Williams but handed out 14 assists for the Jazz, who are 3-0 at home.
The Suns overcame a 26-point deficit against Cleveland on Friday, but couldn't pull off another comeback as Utah held a 52-37 edge in rebounds.
Utah also held a 52-36 advantage on points in the paint and held the Suns to 36.8 percent shooting.
The Suns were down 22 points with 2:45 remaining in the third, but opened the fourth on a 9-2 run to pull within 79-70 on Sebastian Telfair's driving layup with 9:24 left.
Dudley then stole the ball from Tinsley and dunked at the other end with 6:18 left to pull Phoenix within 79-72, and Beasley's follow made it a five-point game.
But Utah's size was too much to overcome.
Jefferson and Millsap both scored six points and had four rebounds in the fourth quarter, shooting a combined 6 of 9.
Gordon Hayward added 18 points for the Jazz but was just 6 of 17 shooting and committed four turnovers.
The Suns quickly found themselves down Saturday.
Utah led 29-19 after one quarter, and was up by as many as 16 in the second.
The Jazz got off to a fast start behind Jefferson, who opened 4 of 5. Jefferson had more points in the first four minutes Saturday (six) than he did in a 20-point loss to Denver on Friday (four), when he shot just 1 of 9. He finished 12 of 20, with a pair of blocks and assists.
He also got help from Utah's other bigs.
Derrick Favors' score after a behind-the-back dribble in the lane bumped Utah's lead to 22-11 with 4:20 left, and Enes Kanter's jam off an alley-oop pass from Tinsley gave Utah a 14-point lead.
Favors hit back-to-back shots to open the second quarter and Kanter's impressive move on Markieff Morris in the paint bumped Utah's lead to 35-19.
But after shooting 52 percent in the first, the Jazz went cold, hitting just 1 of 6 from 3-point range in the second and shooting 38 percent overall. Favors' aggressive shot-blocking also got him in foul trouble, as he picked up his third with 8:12 left before half after opening 3 of 4 with three blocks.
As they did Friday, the Suns chipped away.
They were down just 50-43 at halftime even though Utah held a 28-15 rebounding advantage and 30-16 edge on points in the paint.
The Suns saw the game get out of control quickly in the third with Millsap and Jefferson doing much of the damage.
Millsap scored on a driving layup, then sank a free throw on the next possession to give Utah a 20-point lead with 3:44 left in the quarter.
Favors' dunk made it 77-55, and the Jazz took a 77-61 lead into the fourth. The Suns shot just 27.3 percent in the third quarter while Utah made 10 of 17.