Australia was forced to lodge a review after the umpire refused the tourists lbw appeals on Matt Prior (17), but DRS showed that the ball, which nipped back towards Prior's pads, would have smashed into leg-stump.
The visitors continued their onslaught through Nathan Lyon, who dismissed Jonny Bairstow for 14 with an lbw appeal. The batsman attempted a sweep from Lyon's delivery, but the ball struck his pad heading towards the stumps.
With England in need of an assured innings from Stuart Broad and Tim Bresnan, a counter-attack attempt from Broad went wrong for the hosts as he lofted a shot into the air and comfortably into the hands of David Warner.
Broad was sent packing with just three runs to his name while Swann fell not long after by getting caught out on 13.
Bresnan (12) and James Anderson (16) end the day unbeaten, taking England's score to 238-9.