Burke scored 20 points, including two 3-pointers in the final four minutes, and the Jazz beat the Phoenix Suns 112-104 on Saturday night.
Richard Jefferson added 15 for the Jazz, who were 0-9 on the road entering the contest and lost 112-101 at home to Phoenix on Friday night. Marvin Williams and Derrick Favors added 14 apiece as Utah put seven players in double figures.
Utah has won two of three but has just three victories in 18 games this season. Burke's previous high was 14 in the Jazz's overtime win over Chicago two games ago.
"Our guys thought they could just show up tonight and win the game and in this game it doesn't happen that way, but they don't want to listen to it," Phoenix coach Jeff Hornacek said. "Coaches are telling them they have to be ready and that's what happens."
Burke, a first-round draft pick who was the college player of the year at Michigan, shot 4 of 6 on 3-pointers.
His last 3 put the Jazz up 105-97 with 1:13 to play.
"I wasn't trying to settle for the 3," he said, "I was trying to get in the paint and get a 4- or 5-foot jump shot or make the defense collapse so I could kick it out for an open jump shot."
But he said he saw the Suns get mixed up on a screen "and I was at the 3-point line and had the confidence to shoot it."
The Jazz had trailed by as many as 20 points in their loss to Phoenix on Friday but were either close or ahead throughout this one.
"We felt like Phoenix came into our building and could do whatever they wanted to do," Williams said. "They beat us in transition, they beat us in half court, so we wanted to come in tonight and really focus on those two areas and it really worked out for us."
Utah led by as many as nine points before the Suns finished the first half with a 12-1 run to lead 53-49 at the break.
The Jazz took the lead three minutes into the third quarter and held it the rest of the period, but never by more than four points.
Eric Bledsoe, who scored eight in the period, sank two free throws with 15 seconds left in the third quarter to cut Utah's lead to 78-77 entering the fourth.
Enes Kanter opened the final period with a 4-foot hook shot, then Jeremy Evans sank a 20-footer to give Utah its biggest lead of the half, 82-77. The Suns' Gerald Green nailed a 3-pointer to make it 82-80, then made two in a row to tie it at 86. But Alec Burks scored four in a 6-1 spurt that gave Utah a 93-87 lead with 6:38 to play.
Williams' 3-pointer extended the lead to 98-91 with 5:15 to play. Bledsoe, in his second game back after missing five with a bruised shin, made two free throws to cut it to 98-95 4:09 from the finish, but Burke sank a 3 from far beyond the top of the key and the Jazz were up 101-95 with 3:53 left.
Frye's rebound basket with 3:35 to go cut it to 101-97. After Gordon Hayward made one of two free throws for the Jazz, Bledsoe missed two from the foul line, then Burke made his final 3 to make it an eight-point game. The Suns never got closer than four after that.
"It was definitely frustrating," the Suns P.J. Tucker said. "It was a letdown, especially after playing so well yesterday."
Utah's other two victories have come at home against New Orleans and Chicago. ... After scoring 17 in the first half at Utah on Friday night, Dragic had 14 points and eight assists at the break Saturday. ... Phoenix never led by more than six. ... The Jazz outscored the Suns 25-13 in second-chance points. ... Utah coach Tyrone Corbin was called for a technical foul at the end of the first half, but Dragic missed the corresponding free throw at the start of the third quarter.