He attended the public schools and graduated from Milroy High School in 1926. He then received a teaching certificate from Mankato State College in 1927 and graduated from the University of Minnesota in 1933.
He worked as a school teacher and superintendent for fourteen years and was also an active farmer. Zwach served in the Minnesota House of Representatives from 1934 to 1946. He was elected as a Republican to the 90th, 91st, 92nd and 93rd congresses, (January 3, 1967 – January 3, 1975).
He was not a candidate for reelection in 1974.
He was a resident of Lucan, Minnesota until his death on November 11, 1990. He was buried at Saint Michael’s Cemetery.
Republican Party of Minnesota, Republican Party.
He was a member of the Minnesota Senate from 1946 to 1966 and was the majority leader from 1959 to 1966, leading the Conservative Caucus in the nonpartisan body. He was also a member of the Interim Agriculture Commission, 1955–1957.