The unflappable Clarke was 125 not out from 208 balls at the close after notching the tourists' first ton of the series with a flicked single, while Steve Smith was unbeaten on 70 after a day of fluctuating fortunes that ended with Australia on top.
England, who are 2-0 up in the five-match series and will retain the Ashes at the revamped Manchester venue with a win or a draw, were cheered on by a packed crowd and a lone trumpeter, but some pizzazz was missing from their play and the atmosphere.
Opener Chris Rogers, 35, fell short of his first Australia century when he was trapped lbw by a fullish ball from spinner Graeme Swann for a test-high 84 in the middle session.
"It's huge. As a batting side we've been under pressure," Rogers told a news conference. "Today I guess the pressure was off us a bit and we could play with a bit more freedom."
Replays showed Rogers was right to be given out, but Usman Khawaja's dismissal before lunch was the major talking point.
He was adjudged to have been caught behind off Swann for one but reviewed umpire Tony Hill's decision.
Third umpire Kumar Dharmasena sided with his colleague despite replays showing no obvious edge in the latest decision review system (DRS) dispute to afflict the series and Australia.
"It was disappointing and another question mark. It's people's careers on the line as well so you want decisions to be right," Rogers said.
Shane Watson earlier got away with several loose shots through the slips, over gully and just short of point but was caught at slip by Alastair Cook off paceman Tim Bresnan for 19.
Clarke and Rogers, obeying the message from on high to knuckle down and build an innings after repeated Australian carelessness with the bat this series, were watchful but pounced on any loose bowling as the pacemen struggled with footholes.
"(Clarke) is such a key person in our batting side. If he scores runs it makes it easier," Rogers added.
Clarke was impressive in his 24th test ton if not at his very fluent best having been troubled by spectators above the pavilion sightscreen when taking on Swann, who took two for 82.
Smith survived another minor DRS controversy when England reviewed a not-out lbw decision against Swann and Hawk-Eye said just less than half the ball would have hit leg stump, thus reverting to the umpire's call.
The hosts later wasted their second and final review on Smith when DRS showed he had not edged James Anderson behind. He was then plum in front to Stuart Broad on 24 but Hill said not out.
"We are quite pleased with the way we stuck in there," England's Bresnan said.
"Clarke has left the ball well. He's identified that it's a batting day. It's not done a lot out there."
Australia had lost the toss at Trent Bridge and Lord's, when England batted first both times on their way to victory, and the relief on Clarke's face was visible as the coin landed his way.
The tourists, who risk losing a seventh test in a row and a third straight Ashes series, brought in David Warner at six after the left-hander returned from his banishment to the A squad for punching England's Joe Root in a bar in June.
He replaced the ineffective Phil Hughes, while off-spinner Nathan Lyon came in for left-armer Ashton Agar and paceman Mitchell Starc replaced the injured James Pattinson.
England were unchanged with Kevin Pietersen fit to play.
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- Graeme Swann
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