In 1946, Kazen was elected to the Texas House of Representatives and served from 1947 to 1953. He then served in the Texas Senate from 1953 to 1967, and was elected president pro tempore of the State Senate in 1959. He served as acting governor of Texas on August 4, 1959. He was a member of the Texas Legislative Council for sixteen years.
He was elected to Congress as a Democrat in 1966 representing the newly created 23rd District. It was the largest congressional district in area in the nation (excluding at-large districts encompassing whole states), stretching across 800 miles from El Paso in the west to San Antonio in the east. It had been created when Texas' previous congressional map was thrown out by the United States Supreme Court in the case Wesberry v. Sanders. He was reelected eight more times with no substantive opposition.
In 1984, Kazen's opponent in the Democratic primary was Bexar County Circuit Court Judge Albert Bustamante. By this time, the 23rd had become a majority-Hispanic district. Due in part to the demographic changes in the district, Bustamante upset Kazen in the primary, ending Kazen's 39 years as an elected official. After Kazen's defeat, no non-Hispanic white Democrat represented a significant portion of San Antonio in the House until Lloyd Doggett had his Austin-based district redrawn to include a section of San Antonio.