Joe Root called for "special" contributions and a sustained overall performance as England's campaign approaches a tipping point in Perth, with the urn already on the line at 2-0 down in the five-match series.
Malan's 140 and Bairstow's 119 served up the quality in an England Ashes record fifth-wicket stand of 237.
But then after the tourists lost their last six wickets for 35 in their first-innings 403 all out, Steve Smith's 92 not out and Usman Khawaja's 50 helped Australia to 203 for three at stumps.
Smith was flawless and batted on another level, despite minor vagaries of bounce already as cracks began to appear at the WACA.
Khawaja, however, had luck on his side - notably when Root failed to sight a head-high chance at second slip after an edge off Chris Woakes on 28.
Australia's third-wicket partnership realised 124 and England had to get through the last hour without Craig Overton - off the pitch with a sore side - after his two afternoon wickets kept them competitive.
England had a curious morning. It began with four consecutive maidens, courtesy of Mitchell Starc (four for 91) and Josh Hazlewood (three for 92); yet the first hour ended with four overs which cost 36 runs.
Bairstow completed his hundred in 185 balls, triggering a redemptive and cheeky celebration as he followed several punches of the air with a headbutt for the helmet he had just shed.
The reference to his unconventional greeting for Australia opener Cameron Bancroft, in a Perth bar seven weeks ago, was lost on no one in the ground - and lapped up by most, whatever their partisan persuasion.
Sadly for England, it was the precursor not to further riches but one of their trademark collapses.
Malan was furious with himself for mistiming an attempted big hit at Nathan Lyon close enough for substitute fielder Peter Handscomb to take a diving catch at point.
Moeen Ali was then summarily bounced out for a second-ball duck by Pat Cummins. Woakes got too much on a flick all the way down to fine-leg off Josh Hazlewood, and then Bairstow's intent cost him when he aimed across Starc and lost his middle stump.
The rest was details, and none that favoured England as their tail folded.
Australia's reply began ominously, the new ball rarely hitting anything but the middle of David Warner and Bancroft's bats.
But Overton made a surprising intervention when he found lateral movement and Warner's outside edge for a caught-behind dismissal, then beat Bancroft on the inside for lbw after captain Root rightly called for DRS.
Overton might already have had three wickets, had he clung on diving to his left for a very tough return catch offered by a scoreless Khawaja second ball.
It was barely a half-chance, but in England's current circumstance was at the level they must reach to stay in this series, as Root has correctly identified.
Woakes got his angles spot on to eventually part Smith and Khawaja with a marginal lbw against the left-hander.
But Australia had still regained the initiative by the time Shaun Marsh survived off Moeen as Bairstow and Mark Stoneman converged in vain on a clear-cut chance which looped up off the boot of short-leg just before the close.
Bairstow said: "(On Friday) morning it was pretty tough out there. But I'm delighted to get my first Ashes hundred. It's something as a boy you really want to do. I've been fortunate enough to play in a few Ashes series now - to get it at the WACA, away from home, means a heck of a lot."
The 28-year-old wicketkeeper-batsman completed his hundred in 185 balls, triggering a cheeky celebration as he followed several punches of the air with a headbutt for the helmet he had just shed.
The reference to his unconventional greeting for Australia opener Cameron Bancroft, in a Perth bar seven weeks ago, was lost on no-one in the ground and Bairstow enjoyed the moment.
"There's always some feeling, just a bit of light fun, and that's exactly how it should be taken," Bairstow said of the celebration. "(There's a) huge amount of passion within the game - that's been throughout the series."
Asked whether England had targeted more than 403, he said: "Potentially we could have kicked on and got a few more than that. It's something to say we got 400. After being 100 for four, I think we'd have taken that.
"They played pretty well (on Friday) evening. (Saturday) morning's a crucial session for us, to try to keep them out there for as long as possible and scoring at a rate we're comfortable with.
"At end of the day (on Saturday), who knows what could have happened? They obviously took six wickets in the morning session - there's no reason we can't. The wicket's offering a decent amount as well.
"If we get it in the right areas, with the skills the boys have shown throughout the series, there's no reason why we can't do the same."