Warne took six of the eight England wickets to fall on the final day as England was dismissed for 323 runs in its second innings while chasing 508 for victory.
Warne, who took a record 34 wickets in the Ashes series in England last year, dominated with his sharp turn and immaculate control.
His teammates applauded Warne from the field after Australia took a 1-0 lead in the five-Test Ashes series. It was Australia's first victory under the captaincy of Mark Taylor.
"Shane is a bit of a wizard,'' said Taylor. "It is certainly nice to have him in your arsenal.''
The victory target always looked an improbability for England. The highest successful Test run chase was 406 by India against West Indies in 1976.
England resumed on 211 for two -- 297 runs from victory -- with Graeme Hick on 72 and Graham Thorpe on 66, but slumped after Warne took two key wickets in the first 40 minutes of play.
Warne dismissed Hick and Thorpe, who had shared a dogged third-wicket stand of 160, and helped reduce England to 250 for five at lunch. The visitors added just 39 runs in the opening two hours and lost three wickets.
Warne was at his mesmerizing best after the break, claiming Graham Gooch for 56, Phillip DeFreitas for 11, Martin McCague for a duck and Darren Gough for 10. He dismissed the last four batsmen in the space of four overs.
"Everyone finds an extra 10 percent when they are bowling against England,'' said Warne after being named Man-of-the-Match.
The second Test begins Dec. 24 at the Melbourne Cricket Ground.
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