The tourists need at least a draw to keep the series alive and captain Alastair Cook will resume after the break on 17 not out alongside Michael Carberry, who had scored six on another sweltering morning in Perth.
Mitchell Johnson was soon bowling at the 145 kilometres per hour mark but it was fellow quick Ryan Harris who came closest to taking a wicket, only for Steve Smith to spill a difficult chance to catch Cook in the slips.
Johnson was the first victim of England's pace attack in the morning but despite his departure in the second over of the day, Australia still added 59 runs to their overnight tally of 326 for six.
England bowled a better length than they had in the final two sessions on Friday, when they let the hosts off the hook after reducing them to 143 for five at one stage.
Stuart Broad (3-100) had Johnson caught behind by Matt Prior for 39 and Smith went in similar fashion for 111 after an England appeal to the TV umpire revealed a tiny nick and gave James Anderson his first wicket of the match.
Ryan Harris accumulated 12 runs before pushing an Anderson delivery to Joe Root in the gully but Nathan Lyon (17 not out) and Peter Siddle (21) put on 31 for the last wicket before the latter was also caught behind off Tim Bresnan.
Anderson finished with figures of 2-60 and spinner Graeme Swann 2-71 and England will rue not finishing Australia off when they had them on the ropes on Friday.
Australia lead the five-match series 2-0 after a 381-run victory in Brisbane and a 218-run triumph in Adelaide.