Pitching the ball up and finding some late swing, he removed David Warner, Usman Khawaja and captain Michael Clarke in the space of 27 balls and beat the bat of Rogers on countless occasions.
Warner, promoted to the top of the order after batting at number six in the
drawn third Test at Old Trafford,
was bowled after bringing his bat down too late on a ball that arrowed into his off stump.
Khawaja got a thin edge off the underside of his bat to give Matt Prior his 200th Test catch and a frustrated Clarke and perished to a wild swipe that flew high to Cook at first slip.
There was no let-up from Broad as he had Rogers groping outside off stump before throwing his arms up to celebrate what he thought was a catch behind.
Ashes 2013: Broad feels England need some quick wickets
Umpire Tony Hill upheld the appeal but Rogers successfully reviewed the decision when replays showed the ball struck pad not bat.
With Hawk-Eye suggesting the ball would have clipped off stump, England assumed Rogers would be given out lbw, but because Hill had given him out caught and the lbw prediction was only an "umpire's call", the batsman survived.
The reprieve allowed Australia to scrape through to lunch without further damage, only for Bresnan to reapply the pressure with the wicket of Steve Smith, who poked tentatively and nicked through to Prior.
With the tourists reeling on 76-4, England would have been confident of securing a first-innings lead, but their efforts were fatally undermined by two dropped catches in successive overs.
Watson, fidgety and unsettled against the moving ball, drove a delivery back towards Bresnan, who stuck out a left hand but could not hold on.
Ashes 2013: Chris Rogers delighted with maiden Test century
Then, from the final ball of a superb over, Broad drew a loose drive from Rogers that flew off the edge and was put down at second slip by Swann, diving across Cook, who looked well positioned to take the catch.
Unfortunately for England, the wicketless James Anderson and Bresnan struggled to match Broad's intensity or threat, allowing Rogers and Watson to settle into their rhythm and accumulate runs with greater ease either side of tea.
Watson hit seven fours in his first half-century of the series, while Rogers began to find the gaps in the field to move towards his landmark century.
Broad returned to strangle Watson down the leg side, but Rogers held firm under darkening skies to complete a memorable hundred.
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