After playing in 42 games with the Indians in 1956, Averill spent 1957 and 1958 with the San Diego Padres, where he had his best seasons in the minors. In 1957, he had 19 home runs and 67 runs batted in in 119 games, and he followed that up in 1958 with a .347 batting average, 24 home runs, and 87 runs batted in in 112 games. He was brought back up to the Indians for 17 games, then was traded to the Chicago Cubs with Morrie Martin for Jim Bolger and John Briggs. He spent a season and a half with the Cubs, then was traded to the Milwaukee Braves for Al Heist. After a month of not appearing in a game, he was traded to the White Sox and finished 1960 with them, only to be selected that December by the Los Angeles Angels in the 1960 Major League Baseball expansion draft.
Averill had his best season in 1961 with the Angels. In 115 games, he had a .266 batting average and 21 home runs. The following year, Averill set an MLB record that he shares with Piggy Ward. He had the most consecutive plate appearances reaching a base with 17, which he did from June 3 to June 10, 1962. He ended that season with a .219 batting average in 92 games, then was traded to the Philadelphia Phillies for Jacke Davis. After 47 games with the Phillies, Averill was sent back to the minors, and spent two more seasons with the minor leagues before retiring.