The Jazz climbed past Phoenix into ninth place in the Western Conference playoff race by snapping Houston's four-game winning streak. Utah is only a game behind Denver for the final post-season spot.
Haywood scored 29 points with six assists and Millsap had seven rebounds to go with his 21 points.
Utah led by 18 late in the third period before Houston cut its deficit to four midway through the final quarter. The Jazz closed the game on a 16-8 run.
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