After four-and-a-half years in the minors, he made his major league debut for the Twins in 1971, pitching in 18 games and starting 12, going 2–5 with a 5.03 ERA.

After spending 1978 in the Chicago White Sox organization, Luebber returned to the majors in 1979 with the Toronto Blue Jays.

The Blue Jays released him the following spring, and he was signed to a minor league contract by the Baltimore Orioles.

He then returned to the San Diego Padres farm system between 1986 and 1988, making a number of appearances at the double-A level.

In 1989 he moved on to the Senior Professional Baseball Association, where he pitched two seasons for the Fort Myers Sun Sox.