Cousins, who had missed the final two games of Golden State's just completed four-game trip with a sore ankle, recorded 19 points and 11 rebounds in 26 minutes of action. Klay Thompson had 18 points, and Kevin Durant and Stephen Curry each scored 15 for the Warriors.
Dewayne Dedmon made a free throw with 6.2 seconds left to give the Hawks a 117-114 lead. Utah's Kyle Korver then missed two free throws, the second on purpose, and Donovan Mitchell missed a 3-pointer that was rebounded by Atlanta's Kent Bazemore as the clock expired.
The win broke Atlanta's three-game losing streak and snapped Utah's five-game winning streak. The Jazz got 34 points from Mitchell, his second straight 30-point game.
Detroit's Blake Griffin had 17 points, seven rebounds and eight assists despite shooting 4 of 17 from the field. Andre Drummond supplied 16 points and 19 rebounds, and Luke Kennard also scored 16 points to help the Pistons win for the third time in four games.