England first innings centurion Dawid Malan urged his team to ramp up the pressure on the home side at the end of the first day's play, but a late order collapse by the visitors and the broad bat of Smith ensured the match was evenly poised at the end of the second day.
At stumps Australia were 203 for three, with Smith on 92 and Shaun Marsh on seven, a deficit of 200 runs with seven wickets in hand after dismissing England for 403.
England had looked set to post a massive score when they were 368 for four with Malan and Bairstow seemingly in total control, but then lost six wickets for 35 runs in a stunning collapse before lunch.
Second-gamer Chris Overton (2-46) then raised English spirits again by removing openers David Warner (22) and Cameron Bancroft (25) in quick succession, before Smith again proved a major stumbling block.
Smith was rarely troubled by the English bowlers and played shots to all points of the ground, having faced just 122 balls and hit 14 fours and one six.
Khawaja, who survived a tough caught and bowled chance from Overton before he scored, was adjudged lbw to Chris Woakes for 50, and failed with his third umpire review.
Australia lead the series 2-0 and can regain the Ashes with victory at the WACA Ground, although heavy rain is forecast for the final two days.
Bairstow put a controversial few weeks behind him on and off the field to post his fourth Test century as part of a 237-run stand with Malan, who notched his maiden Test century.
The pair notched a new record fifth-wicket partnership for England against Australia, beating a long-standing mark set in 1938 by Eddie Paynter and Denis Compton at Trent Bridge.
Having come together with England under pressure at 131 for four shortly after lunch Thursday, the pair breathed life back into their team's Ashes defence.
Bairstow's century was a welcome knock for the English batsman after a controversial tour, with a headbutt incident at a Perth bar causing unwanted attention, and a war of words with the Australians on and off the field.
Promoted to six, Bairstow was bowled by Mitchell Starc (4-91) as wickets fell in a rush late in the England innings.
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