After not receiving much interest and writing letters to 40 prospective schools, he received a scholarship offer from Division II Northern Colorado University. He was a four-year starter at defensive tackle and received third-team Little All-American honors in 1975.
Stalls was selected in the seventh round (191st overall) of the 1977 NFL Draft by the Dallas Cowboys. As a rookie he was a core special teams player. In 1978, he was used mainly as a pass-rush specialist at left defensive tackle in place of Jethro Pugh or Larry Cole and emerged as a key reserve, registering 4 unofficial sacks (fourth on the team).
In 1979, he unexpectedly started the first 12 games at left defensive tackle (replacing the retired Jethro Pugh) ahead of former first-round draft choice Larry Bethea, until being replaced by Cole, after the Cowboys traded for John Dutton who would play left defensive end. He finished with 51 tackles and 5 unofficial sacks (tied for fourth on the team).
In 1980, Ed "Too Tall" Jones unretired and the Cowboys opened training camp with 8 quality defensive linemen, when they usually kept seven. The team decided to retain Bethea and Bruce Thornton instead, and traded Stalls to the Tampa Bay Buccaneers in exchange for a 1981 seventh round pick (#173-Ron Fellows) and a 1982 fourth round pick (#101-Brian Carpenter).