Reger Dowell's 3-pointer, with 1:19 left in the second overtime, gave UT Arlington (14-15, 9-8 Sun Belt Conference) the lead for good at 82-80.
Williams made the first two free throws and tried to miss the third on purpose, but the shot banked in and the Mavericks hung on for the one-point victory.
UTA had used a 19-0 run to pull ahead 63-49 with 6:35 left in the second half, and the Trojans answered with a 16-2 run to close out regulation tied at 65.
Hunter Williams had 25 points and Antoine Myers 21 to lead Troy.
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