The Suns (26-25), who have won four straight against Utah, moved above .500 for the first time since Dec. 7 with their sixth win in seven games, spoiling the debut of new Jazz coach Ty Corbin.
Deron Williams and CJ Miles each scored 19 points, but the short-handed Jazz have dropped 11 of 15.
Sloan was a fixture on the Utah bench for 26 years, 23 as a head coach - the longest active tenure in major American professional sports before he abruptly retired Thursday.
The Hall of Famer is the third-winningest coach in NBA history with a record of 1,221-803.
Some said a clash with Williams was to blame for Sloan's departure, but Sloan merely said he had lost the energy needed to coach in his famously intense manner.
When Williams, who openly challenged Sloan at times this season, was introduced before the game, loud cheers were mixed with a measure of boos.
Corbin, a former Jazz player in the 1990s who has been an assistant coach since 2004, received a sustained ovation as he walked into the arena and took his place in front of the Utah bench. Before the game, the new coach admitted he was nervous and joked he might call Sloan at halftime for some advice.
The Jazz were fine in the first half and led 56-44 at the break as Williams handed out nine of his 14 assists.
But the Suns roared back in the third quarter behind Robin Lopez, who had 11 points and five rebounds in the period. Grant Hill's layup capped a 14-5 run that gave Phoenix a 66-63 lead.
Hakim Warrick scored 16 and Marcin Gortat had 12 points and 10 rebounds for the Suns, who outscored the Jazz 51-27 in the second half and won going away.
The Suns consistently beat the Jazz to the ball in the second half and Utah appeared defenseless against Nash and his precision on the pick-and-roll.
Known as an offensive juggernaut in years past, the Suns are now winning with defense. The Jazz managed just 32 percent shooting in the final two quarters and committed 14 turnovers for the game.
Paul Millsap scored 16 points and Gordon Hayward had 14 for the Jazz, who have lost four in a row at home.
When Andrei Kirilenko twisted his right ankle in a scramble for the ball in the second quarter and limped to the locker room, the Jazz were down to nine healthy players. Raja Bell sat out with a strained left calf and Ronnie Price did not dress due to a sprained toe while Francisco Elson played with an inflamed knee.
The Jazz looked energized from the start and raced out to a 13-2 lead. Corbin sat in his seat most of the time, rising only to call a play or remind a player of a defensive assignment.
NOTES: Former Jazz star Karl Malone sat courtside and told reporters before the game he was shocked that Sloan abruptly resigned because "Coach don't quit nothing." ... "Come Home Sloan" and "Can't We Just Kiss and Make Up" were some of the signs lamenting Sloan's departure. ... Kirilenko missed three games in early February with a sprained left ankle. ... Hill and Vince Carter went over to the Jazz bench to offer congratulations to Corbin before the opening tip.