The home side's victory against the ODI and T20 world champions, which came with 19 balls to spare, marked the beginning of Pat Cummins' tenure as Australia's one-day captain succeeding Aaron Finch, who quit the format in September.
Four days after winning the T20 World Cup in Melbourne, England slumped to 66-4 in the 14th over as Australia's pace attack, led by Cummins (3-62), breathed fire with the new ball, vindicating their decision to field.
Phil Salt perished in the slip, Jason Roy and Sam Billings were bowled through the gate while James Vince departed caught behind.
Malan counter-attacked in the middle overs, hitting four sixes -- two of them off the bowling of Cummins -- and 12 fours before holing out in the deep in the 46th over.
David Willey's unbeaten 34 was the next highest score by an England batter as the tourists went on to post a decent 287-9 at the Adelaide Oval.
A 147-run opening stand between David Warner (86) and Travis Head (69) effectively laid the platform for Australia's comprehensive victory.
Chris Jordan broke the stand by taking the wicket of Head while Willey dismissed Warner and Marnus Labuschagne in his successive overs but Steve Smith, who made 80 not out, stayed put and sealed victory, hitting Malan for a six.
The teams move to Sydney for the second ODI on Saturday to be followed by the third and final match in Melbourne on Tuesday.
