The Jazz led by 18 points late in the third period, but collapsed down the stretch after winning their previous two games.
Atlanta held Utah to a single point over the final 2:20 and the Hawks produced the final seven points of the contest.
Ivan Johnson gave Atlanta the lead for good at 96-94 with 1:33 to play by hitting a layup off a feed from Harris.
Randy Foye made six 3-pointers and scored 25 points in leading the Jazz.
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