Lewis converted 6 of 10 3-pointers and the Longhorns (5-2) won their third straight game.
Jordan Reves led Texas-Arlington (3-2) with 15 points but the Mavericks posted their lowest score of the season. UT-Arlington has never beaten Texas in eight attempts.
Texas led 3-2 after a 3-pointer by Lewis about three minutes into the game and never trailed after that.
The Longhorns used 13 3-pointers - eight in the first half - to distance themselves from Texas-Arlington and finished shooting 50 percent from beyond the arc.
Texas was 23 of 51 shooting from the floor against the nation's top field-goal percentage defense. The Mavericks had not given up more than 63 points to an opponent this season. Texas surpassed that mark with 7:54 remaining on a pair of free throws by Javan Felix.
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