The Suns began the restarted competition with the second-worst record among the 22 teams involved but have been undefeated in their five games since to emerge as serious playoff contenders.
Donovan Mitchell scored 35 points for Utah, including a three-pointer with 4.2 seconds remaining in the second overtime which brought the Jazz within reach yet again.
Mitchell then attempted a desperate shot from halfway but could not make the basket.
The Mavs scored the last seven points of regular time to tie up the scores on the buzzer, then forged away for the win over the Bucks, who have already secured top spot in the Eastern Conference.
Luka Doncic scored 36 points for Dallas in his NBA-leading 17th triple-double, adding 19 assists and 14 rebounds.
Milwaukee star Giannis Antetokounmpo had 34 points, 13 rebounds and five blocks before fouling out in the final seconds, on the day the reigning MVP was named a finalist for this year's top award along with LeBron James and James Harden.