Bairstow ton gives England hope after Starc's double strike
But Bairstow counter-attacked superbly and went to his century in style with a legside six off a 90 mph delivery from fast bowler Pat Cummins.
He made 112 before falling to Cummins and England were on 249 for 6 with five overs left.
Bairstow's tenth century in 83 matches at this level came from 116 balls, including 10 fours and two sixes.
He also shared a fifth-wicket partnership of 114 with Sam Billings, whose 57 followed his 118 in England's series-opening loss.
England captain Eoin Morgan won the toss and batted on a fresh pitch with the three-match series all square at 1-1.
But the first ball of the match saw Jason Roy edge a drive off Starc to Glenn Maxwell at backward point.
Next ball, left-arm fast bowler Starc had Test captain Joe Root lbw with an inswinger.
England were 0-2 before left-hander Morgan survived the hat-trick delivery when the ball thudded into his pads.
Bairstow, however, hit Josh Hazlewood for two crunching fours before lofting Cummins for six.
Morgan made 23 before he drove Adam Zampa to Starc at mid-off before the in-form leg-spinner had dangerman Jos Buttler chipped to extra-cover for just eight.
But Billings gave Bairstow excellent support, completing a 53-ball fifty before he too fell to Zampa, when a mistimed reverse sweep lobbed to short third man. Zampa finished with fine figures of 3-51 from his maximum 10 overs.
Australia were again without Steve Smith, the star batsman not featuring at all in this series after being hit on the head by a throw-down from a member of the tourists' coaching staff while batting in the nets last Thursday.
The visitors insisted he was being rested purely as a precaution despite passing two concussion tests.
But, having seen Smith bat in the nets again on Tuesday, they decided against playing him, with Australia captain Aaron Finch saying at the toss: "Steve Smith had a long hit yesterday and pulled up a little groggy. When you're dealing with a head injury, you want to be cautious."
Australia were unchanged but England recalled fast bowler Mark Wood, fit after an ankle injury, in place of left-arm paceman Sam Curran.
That followed a dramatic 24-run win on Sunday when Australia, seemingly cruising to victory, lost their last eight wickets for 63 runs.
This is England's final fixture of a home season overshadowed by the coronavirus. If they win, it will mean they have not lost a series in any format across 18 matches this summer.