On February 3, 1979, he was traded by the Angels along with Brad Havens, Paul Hartzell and Ken Landreaux to the Minnesota Twins for Rod Carew.

Four years later, he was selected to the American League All-Star team in 1984.

During his sophomore season, Engle became the first player to hit a home run in Minneapolis's newly opened Hubert H. Humphrey Metrodome.

This occurred on opening day, April 6, 1982, and also marked the first hit, run scored, and RBI in the stadium's history.

Engle is the brother in-law of his former Twins teammate, Tom Brunansky.