The Blazers (4-7, 3-4) jumped out to a 17-3 lead with 10:24 remaining in the second quarter thanks to a 52-yard touchdown pass from Ellis to Jeffrey Anderson, a 1-yard scoring run by Shed and a 25-yard field goal by Josh Zahn.
Ellis connected with Shed on a 54-yard touchdown pass 1:53 before halftime to extend UAB's lead to 24-6.
Paulo Henriques kicked field goals of 44, 43 and 36 yards for Memphis. The 36-yarder, which came with 20 seconds left in the second quarter, pulled the Tigers (1-10, 0-7) within 15 points, 24-9, at halftime.
Ellis hit Patrick Hearn for a 72-yard touchdown pass in the fourth.
Memphis has now lost 10 games in consecutive seasons and three times since 2006.
Daryl Gross, who spent a decade as Syracuse's athletic director, will start as Division II Cal State-Los Angeles' AD in July.
Freshman DB Chad Clay didn't last long with the Georgia football team, as the Bulldogs dismissed him following a second arrest in the past four months.
Brenda Tracy, who allegedly was sexually assaulted by four men, including two Oregon State players, in 1998 spoke Wednesday to the Nebraska football team.
A man who claims he told Penn State football coach Joe Paterno in 1976 that he was sexually abused as a teen by Jerry Sandusky asked a judge Wednesday to protect his identity and limit questions.
FOX Sports' Bruce Feldman joins The Paul Finebaum Show to share his thoughts on the upcoming National Championship race.
Urban Meyer, Thad Matta and Ohio State athletic director Gene Smith were among the crowd at the parade for the Cleveland Cavliers on Wednesday.