Watch: Dawid Malan century inspires England on Day 1 of Ashes Test in Perth
Middle order batsman was ably supported by wicketkeeper Bairstow following a half century by opener Stoneman.
Dawid Malan said it was time for England to pile the pressure on Australia after his first Test century helped the besieged visitors fight back on the opening day of the vital third Ashes Test in Perth on Thursday.
After Joe Root won the toss and elected to bat, Malan's unbeaten 110 helped the tourists to breathe life back into their Ashes defence by countering hostile Australian bowling on a bouncy wicket at the Waca Ground, which is hosting an Ashes Test for the last time.
At stumps, the visitors were 305-4 after their best day of the series, and Malan said the challenge for England was to grasp their chance.
"We've just not capitalised on the crucial moments," Malan said of the series thus far.
"The first hour tomorrow is crucial for us and if we give them any sniff with the second new ball, we will give the momentum right back to them," he added.
"We will have to be quite ruthless in the way we play tomorrow morning."
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As one of the players identified as suspect going into the series and after failing to get a big score in the first two Tests, Malan said he was relieved to get the monkey off his back.
"I was under a bit of pressure coming into the game so it was nice to score some runs," he said.
"It was nice to do it when the team needed it and cash in when I made a start."
Malan admitted it was tough when he came to the crease against the rampaging Australian fast bowlers, but said he enjoyed the challenge.
Already down 2-0 in the five-match series, the visitors were wavering at 131-4 against some fiery pace bowling after lunch, but Malan steadied the innings with an unbroken 174-run stand for the fifth wicket alongside Jonny Bairstow (75 not out), England's highest partnership of the series.
England overcame the controversial dismissal of opener Mark Stoneman for 56 on a third-umpire decision, and their cause was helped by some generosity from the Australian fielders, who dropped three catches and missed a run out.
Malan was one of the chief beneficiaries as the 30-year-old batsman notched his first century in his eighth Test, and England's first hundred of the series.
He would have been run out for 32 had David Warner managed a direct hit, and was dropped by Cameron Bancroft in the slips on 92.
He steadied his nerves to reach a century with a powerful pull shot off Josh Hazlewood, having faced 159 balls in 221 minutes at the crease, hitting 13 fours and one six.
Malan came to bat with England under pressure against short-pitched bowling from Hazlewood, Mitchell Starc and Pat Cummins, who terrorised the tourists with aggressive bowling that was often more than 145 kilometres (90 miles) per hour.
Stoneman was dropped twice on 52 and struck on his helmet by a fierce delivery while on the same score.
He survived all that, only to be contentiously given out for 56.
The opener fended at a sharply-rising delivery from Starc and wicketkeeper Tim Paine pulled off a brilliant one-handed catch, but on-field umpire Marais Erasmus turned down the Australian appeal.
The hosts called for a review and third umpire Aleem Dar took little time overturning the original decision, although there did not appear to be any conclusive evidence to support the reversal.
The decision clearly upset the England camp, with Root and fielding coach Paul Collingwood coming out of the dressing rooms to voice their concern as Stoneman trudged off
Unfortunately for England, former captain Alastair Cook's form woes continued when he was trapped leg before wicket by Starc for just seven, on his landmark 150th Test appearance.
Cook has more than 11,000 Test runs, but the former England captain has scored just 69 in this series at a rate of 13.80.
Updated: December 14, 2017 05:56 PM