Paul Millsap started 7 of 7 for Utah and finished with 14 points, and Jamaal Tinsley had 12 on 6-of-8 shooting.
Tinsley started in place Mo Williams, who learned earlier in the day he will be out six weeks after opting for surgery on his right thumb.
The game marked the return of Andrei Kirilenko, who played 10 seasons for the Jazz before being allowed to leave via free agency two years ago.
The crowd warmly welcomed the small forward nicknamed AK-47 with a round of applause during introductions. He hit his first three shots but finished with just 12 points on 4-of-7 shooting.
Alexey Shved and Kevin Love led Minnesota (14-14) with 13 apiece and Love added 10 rebounds but neither shot well. Love was 4-of-14 shooting and Shved shot 3 of 10
Nikola Pekovic had 11 points for Minnesota.
The Timberwolves made just 29 of 84 shots, including 2 of 17 from beyond the arc. The made only 12 of 40 shots in the second half. They were outscored 56-36 in the paint and 25-8 on the break.
Utah (16-17) trailed by one after the first quarter but opened the second on a 15-4 run and the third on an 11-0 run.
They led by as many as 20 in the third quarter, and unlike last week when they blew a 19-point lead against the Los Angeles Clippers, they kept pouring it on.
Six Jazz players scored in double figures, the kind of effort they will need if they hope to climb back into the playoff picture.
Millsap, who has seen his playing time decrease with the emergence of Derrick Favors, missed his only shot midway through the fourth quarter before exiting for good.
Marvin Williams added 11 points and five rebounds for Utah.
The Jazz were reeling before the game after learning Mo Williams would be out for so long.
But coach Tyrone Corbin and his players expressed confidence in veteran backups Tinsley and Earl Watson.
Tinsley showed his leadership, making 5 of 6 shots in the first half, including one where he bounced the inbounds pass off the backside of Pekovic for an easy layup.
Watson finished with nine assists, including five in the first half when the Jazz led by as many as 10.
The Jazz opened the second quarter on their first big run, with reserves Kanter and Watson providing the biggest punch.
Kanter hit an outside jumper, jammed after a long pass from Watson and went coast-to-coast on a steal for another dunk.
The heady Watson fed players for alley-oops and pushed the ball up the court with long passes, including one that resulted in a Hayward dunk and 40-30 Jazz lead.
Utah dominated on points in the paint, holding a 32-18 first-half advantage.
The Timberwolves also shot just 38.6 percent in the first half, including 1 of 8 from beyond the arc as they trailed 53-45 at the break.
Kirilenko, who was drafted in 1999 by the Jazz (24th overall pick), acknowledged he wasn't sure what kind of a reception he would receive.
While the fans were kind, the opposing players were too much for the T-Wolves.
Utah was motivated after enduring tough back-to-back losses against the Clippers to close out 2012.
They started 2013 on a much better note.