Jaycee Carroll also scored 15 for the Aggies (19-9, 8-4).
James Powelland Alex Harris scored 20 points apiece to lead the Gauchos (20-7).
After falling behind by 10 points early in the second half, UCSB got within 51-48 with 6:16 to play. But three quick fast-break baskets by Wesley and Wilkinson and free throws by Carroll pushed the Aggies back ahead by double digits.
Carroll came into the game shooting 52.8 percent from the field and more than 50 percent from 3-point range, but was only 5-of-13 with one 3-pointer against the Gauchos.
Despite committing 11 turnovers in the first half while UCSB had only three, Utah State led most of the first half. The Aggies outrebounded UCSB 21-15 and held a 28-24 lead at halftime.