The tourists, who lost their last six wickets before lunch, had the Australians on the ropes with three batsmen out in the middle session, including the prized scalp of Warner.
At tea, Australia were 76 for three off 24 overs, with skipper Steve Smith on 19 and Peter Handscomb on 14.
Smith was Australia's big hope and under pressure for a high score after Australia suffered a familiar batting order malfunction.
Warner attempted to pull newcomer Jake Ball through the leg-side only to find Dawid Malan at short mid-wicket for 26 off 43 balls.
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That left the Australians on a shaky 59 for three after the dismissals of debutant opener Cameron Bancroft and the misfiring Usman Khawaja.
Bancroft lasted 19 balls in his first Test before he edged a Stuart Broad lifter outside off-stump for five in the fourth over.
Bancroft forced his way into the Test side at the expense of Matthew Renshaw on the weight of prolific scores in the Sheffield Shield for Western Australia, including an unbeaten 228.
Earlier, England lost six wickets for 56 to fold for 302 all out in their first innings at lunch.
The tourists were looking solid in an 83-run partnership between Dawid Malan and Moeen before Malan's dismissal triggered a clatter of wickets.
Root's team tumbled from 246 for four to be all out with fast bowlers Mitchell Starc and Pat Cummins each taking three wickets and spinner Nathan Lyon two.
Malan, the Middlesex left-hander, hit 11 fours in his third Test fifty off 130 balls in his first Ashes Test before he top-edged a Starc lifter and was caught by Shaun Marsh at deep square leg for 56.
Lyon, who was proving a handful with his drift and turn, struck again with the first ball of his next over, bowling Chris Woakes for a duck.
Wicketkeeper Jonny Bairstow followed shortly afterwards for nine, as he dollied Cummins to Tim Paine for the gloveman's first catch after seven years in the Test wilderness.
Jake Ball smacked three fours before he was snapped up by a diving Warner at leg slip off Starc for 14, and Broad was dropped by Marsh before he went for 20 to an outfield catch by Handscomb.