Dawid Malan followed Mark Stoneman in making his first century in an England kit as his 109 helped the tourists pile up 515 in their final tour match before the start of the Ashes.
Malan's century continued a fine run of form that has seen him pass 50 in every innings on tour so far, while skipper Joe Root made 83.
However, England's lower order suffered a wobble that saw five wickets fall for 38, including a third duck of the tour for Somerset all-rounder Craig Overton, who has been expected to make the Test side.
A last-wicket stand of 58 between Chris Woakes and Mason Crane took England to a first innings lead of 265, and the young legspinner took a wicket when the Cricket Australia XI batted again. Moeen Ali also struck twice, but the seam bowlers made little impact on a slow pitch likely to bear little resemblance to the surface the first Test in Brisbane will be played on.
The Cricket Australia XI reached 121-3 in their second innings and with a day to go, England have a big opportunity to force a morale-boosting win before they enter the white-hot atmosphere of the Gabba.
Fans booking corporate hospitality for next summer's England v India Test at Edgbaston - another ground known for its raucous and partisan atmosphere - will hope England can come through the experience of playing at the ground nicknamed the 'Gabbatoir'.
Some encouragement may be taken from the selection of the Australian squad for the first two Tests, which has seen some controversial selections.
The most contentious has been the choice of Tim Paine as wicketkeeper, seven years after he played the last of his four Tests to date. He does not currently keep for Tasmania, yet replaces the man who does, Matthew Wade. Most had expected Peter Nevill to be picked instead.
Critics in Australia are also unhappy with the selection of veteran Shaun Marsh to bat number six.
Australia's squad has seen six players dropped from the team that played their most recent Test in Bangladesh, with English-born opener Matt Renshaw making way for Cameron Bancroft, who will make his debut in Brisbane and played for Gloucestershire in the recent summer.
He was included after recently making a double century for Western Australia in the Sheffield Shield.
Image: Getty, from Keith Prowse subscription