In 1953, he teamed up with fullback Dave "Kosse" Johnson (the nation's second leading rusher), to win a share of the Southwest Conference title with the University of Texas, while registering 833 rushing yards with a 7.3-yard average, which led the nation. In the 1954 Cotton Bowl Classic against Alabama, Moegle was involved in one of college football's most famous plays. With Rice leading 7–6, Moegle broke through on a sweep from Rice's five-yard line, and was running down the sideline in front of Alabama's bench on his way to a touchdown. Alabama's Tommy Lewis, without putting on his helmet, jumped off the bench and tackled Moegle. Seeing what happened, referee Cliff Shaw awarded a 95-yard touchdown on the play, and Rice went on to win the game 28–6. Moegle finished with 265 rushing yards, which was a Cotton Bowl Classic record until the 2008 game when Missouri's Tony Temple rushed for 281 yards. He finished with game records of 265 yards on 11 carries for an average of 24.1 yards per attempt and 3 touchdowns. Moegle and Lewis later appeared on "The Ed Sullivan Show" to talk about the play.