The West Australian is the first specialist spin bowler to take the new ball in the first innings for Australia since 1938.
James Pattinson (1-6), playing in his first Test since breaking down after the clash with India in Sydney in January, also had a great day back in the baggy green.
The 21-year-old combined with Michael Hussey in a vital 89-run seventh wicket stand to take Australia's score past 300, scoring 32 as Hussey top-scored with 73.
Pattinson then struck with his first ball, claiming Kieran Powell lbw for 19 though replays showed the ball had pitched outside leg stump and the Windies batsman would have been reprieved if he had reviewed the decision.
The late drama overshadowed Australia's innings, which was twice interrupted by rain, with Kemar Roach claiming the third five-wicket haul of his career to finish with 5-105.
Windies spinners Narsingh Deonarine and Shane Shillingford took the other wickets.
Deonarine finished with 2-32 including the vital wicket of Hussey which ended the partnership with Pattinson to go with his capture of Clarke on day one.
Shillingford, who was unlucky not to get Hussey on 47 when wicketkeeper Carlton Baugh bungled a stumping opportunity, finished with 3-92 in his first Test since late 2010.
Play resumes at 0930 on Wednesday (2330 AEST).
-AAP