His play was limited in his sophomore season (1952), after he was lost with a hand cut he suffered trying to open a classroom window that was stuck.

In the 1954 Cotton Bowl Classic against Alabama, Moegle was involved in one of college football's most famous plays.

Seeing what happened, referee Cliff Shaw awarded a 95-yard touchdown on the play, and Rice went on to win the game 28–6.

On March 13, 1960, he was traded to the Pittsburgh Steelers in exchange for a first-round draft choice (#6-Jimmy Johnson).

On December 21, he was traded to the Dallas Cowboys in exchange for offensive tackle Dick Klein and safety Bill Butler.

[6] After being acquired by the Cowboys in part for being a famous player in the state of Texas,[7] he was named the starter at safety in 1961.