The champions reached third day stumps at 331 for five in reply to Queensland's 266 after the entire second day's play was washed out on Sunday.
Clarke, dropped for the third Test against the West Indies, hit 13 fours in his 182-ball knock and shared in a 171-run partnership for the fourth wicket with Dominic Thornely, who made 86.
In Melbourne, Victoria held a 78-run lead over South Australia at the end of day three.
A 184-run partnership between Jason Arnberger and Lloyd Mash turned a first-innings deficit into a lead, and the home side ended the day on 318 for four in its second innings.
Arnberger made 149 and Mash was out for 94, just short of his maiden first-class hundred.