[1][2] Quinn was a member of the Massachusetts House of Representatives from 1957 to 1969 and the speaker of that body from 1967 to 1969.

During his tenure in the house, he played a role in the founding of the University of Massachusetts Boston by co-sponsoring the legislation that established the university in conjunction with Massachusetts Senate Majority Leader Maurice A.

[2][3] Quinn was elected Massachusetts Attorney General by the Massachusetts Legislature sitting in Joint Convention following Elliot Richardson's selection as Under Secretary of State.

[2] Quinn sought the Democratic nomination for governor in 1974, but was defeated by Michael Dukakis.

[2] Following his defeat, co-founded the Quinn and Morris law firm and was a prominent lobbyist.