Because of his lack of playing time at UCLA, few NBA teams had interest in Eaton after he finished his college career. However, the Utah Jazz saw him as a potentially dominant defender and selected him with the 72nd pick in the fourth round of the 1982 NBA draft. Utah coach Frank Layden would later explain his choice by quoting Red Auerbach's old axiom, "you can't teach height". In his rookie season, Eaton made an immediate impact. He replaced Danny Schayes as Utah's starting center early in the year, and finished the season with 275 blocked shots (a franchise record) in 81 games. His 3.40 blocks per game ranked third in the NBA, behind Atlanta's Wayne "Tree" Rollins and San Diego's Bill Walton.