Ian Bell's career-best 141 had powered England to 303-8 but they were left to rue their inability to score freely during the closing stages, which Australia used superbly to claim victory.
Stand-in captain Smith, who scored four centuries against India during their recent 2-0 test series win, continued his rich vein of form to complete another ton on his one-day international captaincy debut, his third in the 50-over format.
Shaun Marsh (45), who replaced the injured David Warner, and Aaron Finch (32) gave Australia the ideal platform for the chase with a brisk opening stand of 76.
England fast bowler Steven Finn, who took five wickets on Tuesday to destroy India, dismissed Marsh and Cameron White (0) in three deliveries leaving it to Smith to resurrect Australia from 92-3.
The 25-year-old Smith looked unperturbed, adding 69 with Glenn Maxwell (37) for the fourth wicket and another 55 with James Faulkner (35) for the fifth to take Australia closer.
Smith, who hit six fours and a six, and Haddin then batted sensibly during their 81-run stand and took the attack to the bowlers once the victory was in sight.
Earlier, put in to bat by Australia, Bell and Moeen Ali (46) added 113 for the opening wicket to give England a flying start.
An aggressive Bell, who hit 15 fours and one six in his 125-ball innings, appeared in good touch and took a firm step towards securing the opener's role for the Feb. 19-March 29 World Cup ahead of Alex Hales.
He timed the ball sweetly, reaching his half-century in 42 balls and then the three-figure mark in 92 balls with a pulled single off paceman Pat Cummins.
Cummins was punished by Moeen early on when the left-hander pulled the bowler for three consecutive sixes.
Bell also added 121 for the third wicket with Joe Root (69) but medium pacer Gurinder Sandhu pulled things back for Australia by dismissing the centurion and England captain Eoin Morgan for a golden duck in three balls.
England lost six wickets in the last nine overs, including three in the last three deliveries of their innings.
(Reporting by Sudipto Ganguly in Mumbai; editing by Amlan Chakraborty and Martyn Herman)
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