The Hawks had an 86-81 lead as the game entered its final stages but they were unable to produce another point. Millsap's layup came with 3:19 to play and Deron Williams finished the run by making two free throws with 6 seconds left.
Utah has won four in a row and all of them have been comeback affairs. The Jazz trailed by at least 10 points in the second half of all four contests and three of the wins have come on the road.
Williams scored 24 points and had 10 assists. Al Jefferson chipped in 15 points and 10 rebounds.
Joe Johnson led Atlanta with 23 points. The Hawks have lost four straight after opening the season 6-0.