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.
A lawsuit alleges that the University of Tennessee has violated Title IX policies and created a "hostile sexual environment" through indifference toward sexual assaults by student-athletes.
Ian O'Connor, senior writer at ESPN.com, joins The Paul Finebaum Show to discuss Roger Goodell's response to safety concerns in the NFL.
Stanford defensive line coach Randy Hart is retiring after 46 years as a college coach.
The SEC doesnâ
The SEC is trying to get the NCAA to stop Michigan from practicing in Florida over spring break.
The Ducks have been very good under Mark Helfrich, but the bar is set very high in Eugene and 2016 could be a pivotal season.