SMU quarterback Bo Levi Mitchell was 29 of 45 for 351 yards a touchdown, but was intercepted three times as the Mustangs (1-5, 0-3) lost their fourth straight.
SMU receiver Aldrick Robinson had 10 catches for a career-high 210 yards, including a 94-yard scoring pass from Mitchell that drew the Mustangs within 24-17 with 13 minutes left in the game.
The Mustangs flubbed an onside kick attempt on the ensuing kickoff and UCF put the game away when Greco found Williams in the end zone with 1:34 remaining in the game.
The teams traded field goals and long scoring drives in a first half that ended 10-10.
SMU's Andrew McKinney bulled in from 1 yard out to finish off a 77-yard drive and Thomas Morestead booted a 33-yard field goal to give the Mustangs a 10-3 first-quarter lead.