Young drained five 3-pointers and Randle notched 10 rebounds, helping the Wildcats (4-1) pull away in the second half.
Willie Cauley-Stein came off the bench to record a double-double of 14 points and 10 rebounds.
The Mavericks (2-3) were led by Brandon Edwards with 24 points.
Reger Dowell added 20 for UTA.
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