The Knights (5-2, 3-0 Conference USA) forced three Memphis turnovers, including a fumble on the UCF 1-yard line in the first quarter.
Murray, starting for the first time since the season opener, had 23 carries and scored twice early. He followed a 1-yard run with an 83-yard romp that was the second-longest run from scrimmage in school history.
Bouye had another big play when he recovered a fumble and ran 79 yards for a 28-10 UCF lead.
The Tigers rushed for a season-high 240 yards behind a career-best 88 yards by Jan Steib.