Root and Bairstow find their form in Ashes warm-up
Joe Root (75) helped the tourists to 418 all out and a first-innings lead of 114 by mid-afternoon on day three.
Root combined with fellow Yorkshireman Jonny Bairstow, who made 48, in a stand of 106.
But Stuart Broad, Steven Finn and Boyd Rankin were then all unable to deliver a telling early blow and it was only thanks to Graeme Swann, and batsman misadventure, that the tourists first managed to get rid of Aaron Finch (59) before a general improvement from their seamers was rewarded with a stumps total of 153 for four.
Finn, in particular, did not initially enhance his prospects of a place in the first Test with a three-over new-ball spell which began with successive fours by Ed Cowan from the first two deliveries - a pull, then a cut - and cost 20 runs in all.
A previously out-of-form Finch took most advantage, however, dominating the scoring with a 43-ball 50, which he completed with his 10th four in the final over of the afternoon off Finn.
In early evening, Finch slog-swept Swann high over midwicket for six but went to the very next ball with an attempted repeat and instead lobbed the ball off an outside-edge into the hands of Michael Carberry at point to end an opening stand of 81.
There remained little in the pitch and success did not come easy against batsmen of the calibre of Cowan and number three Callum Ferguson.
As Finn continued to toil, and Broad was not as effective as in the first innings, there was perhaps a glimpse of collective limitations in the absence of the rested James Anderson until England’s seamers upped their game, each rewarded with one wicket as they bowled in tandem with Swann and under cloud cover.
Broad clean-bowled the stubborn Cowan from round the wicket, beating the left-hander’s back-foot defence.
Kurtis Patterson then escaped on four when he edged Finn high to first slip where Jonathan Trott, standing in for an over while captain Alastair Cook briefly left the field, could not hold the chance.
But Finn was rewarded with the wicket of Ferguson, when he jagged one back to bowl him between bat and pad, and then Rankin had Ben Rohrer edging a faulty pull behind.
England, trying to jockey a position for a timely victory to send them on the way to Brisbane for next week’s Ashes opener, had begun a showery morning on 302 for five.
Their progress was stalled by rain and in addition an extra five-minute stoppage while Root had treatment to his right little finger.
He took a glancing blow on his hand as an awkward delivery from left-armer Josh Lalor followed him and ended up hitting him in the box.
Pain-killing tablets were required and Root was to spend time off the field in the early stages of the hosts’ second innings, but if there was an injury scare it appeared short-lived.
Around 50 minutes were lost in three breaks for rain before lunch, yet Root nonetheless combined with Bairstow in a stand of 106 which extended into early afternoon.
He quickly recovered his composure after the painful blow from Lalor and completed England’s quickest 50 of the innings, off 67 balls, with his sixth four a memorable straight-drive off Chris Tremain.
Bairstow, deputising here for Matt Prior who remains a doubt for the Gabba because of his torn left calf, also negotiated the second new ball.
But he could not quite complete England’s fifth half-century of the innings, falling two runs short when he went after a short ball from Tremain but did not have the required width and edged behind.
England’s last five wickets fell for just 46 in under 10 overs, a flurry which stopped them taking a stranglehold on the match.
Broad poked a catch to cover and Root - perhaps under orders for more quick runs - was bowled, pulling at Nic Bills (three for 76).
But long-suffering leg-spinner James Muirhead was the main beneficiary of English urgency, picking up the last two wickets to finish with four for 115.