Clarke (148), already averaging more than 100 runs per innings at his most fruitful venue, batted wonderfully after some early fortune as he and Haddin (108no) powered Australia to a teatime 516 for eight on day two.
England did not help themselves with some more sleepy and costly work in the field, but nothing went right for them either.
Even when it seemed Ben Stokes had broken the sixth-wicket stand at 111, Haddin caught-behind pushing forward, instead Marais Erasmus checked for a no-ball which was confirmed by video replay.
After Haddin therefore retraced his steps to the middle, there was an ugly reprise of the antagonism which marred the first Test in Brisbane, as batsman and bowler engaged in a verbal confrontation at the end of the over and had to be spoken to by Erasmus.
Clarke was unfazed, and duly reached his second hundred of the series in Stokes' next over - his 26th in all, and seventh in the Ashes.
He was not done yet either, batting well into the afternoon, until he did become Stokes' first Test victim - chipping the first delivery of a new spell to midwicket off a leading edge to end an exemplary, near six-hour innings having hit 17 fours from 245 balls.
There was to be no revenge for Stokes against Haddin, though, the wicketkeeper-batsman instead completing his hundred off the debutant with a fierce pull for his 11th four to add to four sixes.
England had resumed on a cloudy morning hoping they would not pay a high price for the catches dropped the previous evening.
Clarke, of course, had the opposite agenda - and it was he who prevailed as Australia, already 1-0 up in this series, piled on England's misery.
The Australia captain was out to impose himself from the outset against Monty Panesar, and immediately squirted two runs just over and wide of cover to complete his 50.
Clarke might easily have gone without addition to his overnight score, after failing to get to the pitch and chancing his arm nonetheless - but thereafter he was masterful.
Haddin's first runs of the day took him to 1,000 against England, on his way to the fifth half-century of the innings.
Yet quicker reactions in the field might twice have helped see him off on 18 and then 30.
Michael Carberry, at fault when he put down the straightforward catch at point to reprieve Haddin on just five on Thursday, was unable to deliver the right throw for a possible run-out after a quick single to short third-man; then Panesar could not make enough ground to take the catch after a faulty hook at James Anderson.
Clarke had one dicey moment, on 91, when Ian Bell was unable to cling on to an especially tough chance at short-leg as the batsman advanced to Swann and got a thick inside-edge.
For good measure, Clarke also managed to regain his ground before the ball could be ferried back to the stumps by Bell and wicketkeeper Matt Prior.
England's suffering was not yet complete - and even after Clarke was gone, Haddin kept sweeping the spinners to shreds and carving the pace too as he and the tail took the hosts past 500.
:: Both teams and the crowd observed a minute's silence before start of play, and the players took the field wearing black armbands, in tribute to former South African president Nelson Mandela who died on Thursday.