When the Whitlam government won office at the December 1972 election, Wriedt (associated with the ALP's right wing) became Minister for Primary Industry.

On 14 October 1975, Rex Connor was obliged to resign as Minister for Minerals and Energy, as a result of the Loans Affair, and Wriedt was appointed in his place.

[4] Wriedt remained in the Senate until his resignation in September 1980 to contest the House of Representatives seat of Denison at the 1980 federal election; he was defeated by sitting Liberal MP Michael Hodgman.

At the 1986 state election, Wriedt was unable to defeat the incumbent Liberal government of Robin Gray; Labor actually suffered a small swing.

He was the father of a subsequent Tasmanian House of Assembly member, Paula Wriedt.