The previous record of 153 had stood since 1978 but 24 points from Bojan Bogdanovic and a further 23 from Jordan Clarkson off the bench helped break the previous benchmark.
The 49-point win was also the largest margin of victory in franchise history.
The historic win snaps a two-game losing streak for the Jazz but the victory means Utah stays first in the Western Conference.
In total, eight players scored in double figures including Jazz forward Georges Niang.
“I don’t think I’ve ever seen a 150 on the board before,” he said after the game. “We wanted to come out here and make a point.”
Despite a pair of losses in their previous games against the Minnesota Timberwolves, Jazz head coach Quin Snyder said his side had shown good potential.
“I’m probably in the minority, but I actually thought we played well the other night. We didn’t shoot it well,” he said after the match.
“We were solid tonight. And, obviously, we made shots.”
Elsewhere, the Phoenix Suns secured their first playoff berth since 2010 with a 109-101 victory over the Los Angeles Clippers on Wednesday.
Point guard Chris Paul was a major influence in the Suns’ playoff push, recording 28 points, 10 assists and three steals against the Clippers.
The achievement marks yet another landmark in the franchise’s resurgence.
“To be so close last year and to be in a position to clinch a spot now, it’s a blessing and I don’t take it for granted at all.”