The left-hander slammed his 18th Test hundred and third at the Sydney Cricket Ground off 78 balls to reach three figures in just 117 minutes with 17 fours.
At tea after winning the toss, Australia were 224 for two with Warner's opening partner Matthew Renshaw within sight of his first Test hundred on 83 and skipper Steve Smith, playing in his 50th Test, not out 12.
Warner became the first Australian since Bradman 87 years ago to make a century in the opening session on the first day, and the only person to achieve the feat during a Test match in Australia.
"That's obviously an honour and privilege to be amongst the greats of the game," Warner said.
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"It's great to be out there with those guys. Hopefully I can continue with that great start and positive approach."
The only other player to post a century before lunch on the first day of a Test was Pakistan's Majid Khan (108) against New Zealand in Karachi in 1976.
Warner said reaching three figures before lunch was not paramount, but that he felt the adrenalin rising as the century drew closer.
"It wasn't nerve-racking. I told the youngster (Renshaw) with a couple of minutes to go we have to knuckle down and get through to lunch and be patient," he said.
"Obviously as a batsman when the adrenalin is pumping and you know it's around the corner you are probably always going to have a dig."
Warner was finally out 20 minutes after lunch, caught behind by Sarfraz Ahmed off Wahab Riaz for 113 off 95 balls with 17 fours.
Vice-captain Warner has now scored 5,206 runs in 60 Tests at an average of 49.11.
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