Warner carried on where he left off at Lord’s last week, bludgeoning his way to a 108-ball ton before retiring out, with fellow opener Marsh doing likewise after passing three figures in a more watchful innings which may have boosted his chances of a call-up for the third Ashes Test at Edgbaston next Wednesday.
Marsh’s younger brother, Mitchell, and fellow all-rounder Shane Watson both chipped in with half centuries, but skipper Clarke was able to contribute only 16 before falling to the excellent Will Davis on his first-class debut.
Clarke was Davis’s maiden wicket, while the teenager also snared Adam Voges and wicketkeeper Peter Nevill en route to figures of three for 63 as Australia closed on 413 for nine.
The tourists were without injured opener Chris Rogers, while batsman Steve Smith and pace trio Mitchell Johnson, Mitchell Starc and Josh Hazlewood were rested after starring in the 405-run victory over England that levelled the Investec Series.
It meant a return for Brad Haddin, who missed the second Test for personal reasons, with he and Nevill scheduled to share wicketkeeping duties.
After Clarke opted to bat first, there was a sense of deja vu as Australia, led by some fluent strokes from Warner, set off at a brisk pace, as they had done at Lord’s last week, bringing up the 50 inside the first 10 overs.
Derbyshire may have been regretting their decision to leave left-arm paceman Mark Footitt out of the side as their bowlers toiled, with Warner bringing up his 50 off just 55 balls following a mis-field at mid-off.
The left-handed opener, who thumped a fluent 83 in the second innings against England last week, continued to pile on the runs and he reached his century with a thumping drive past extra cover for his 13th four.
After soaking up the applause, he immediately retired out to end an opening stand of 154, allowing Clarke the chance to find some much-needed form ahead of the third Test.
Soon after Shaun Marsh brought up his 50, Clarke got off the mark with a sumptuous four. It proved to be a false dawn, though, as he fended Davis to Tom Knight at second slip to depart for 16.
Derbyshire were celebrating again in Davis’s next over when Adam Voges was trapped in front for just one. That brought Mitchell Marsh out to join his sibling and the two set about steadying the innings, both batsmen smashing sixes to set the tone for a quickfire 78 partnership.
The elder Marsh, who will be waiting in the wings if Rogers is unable to recover from his injury, proved he is ready for a Test return after bringing up his hundred off 177 balls before walking off.
Nevill was only able to contribute a solitary run before he became Davis’s third wicket after driving uppishly to point, while Mitchell Marsh was caught down the leg side for 53 to give left-armer Harry White a wicket on his first-class debut.
Watson, dropped from the side after a poor first Test, laid a marker down with a brutal 39-ball 50, brought up with back-to-back sixes off slow left-armer Knight. But the all-rounder perished for 61, with White getting another wicket from a caught-behind down the leg side shortly after the second new ball was taken.
Haddin contributed 32 before he was cleaned up by Tony Palladino.
Peter Siddle was run out after a mix-up with Pat Cummins (21no), who marked his first first-class appearance in nearly two years by clubbing four fours off the final over of the day to take Australia past 400.