New captain Morgan (121) was the standout batsman, securing his seventh ODI hundred and third against Australia after entering the fray with England in disarray at 12-3.
Ian Bell and James Taylor were trapped lbw by Mitchell Starc with the first and third balls of the game respectively as the tourists sunk to 0-2 at Sydney Cricket Ground after winning the toss.
But Morgan, supported admirably by England’s middle and lower order, played a captain’s knock to set Australia a working total.
Bell (0) scored 187 in England’s warm-up game against the Prime Minister’s XI on Wednesday but collected a golden duck at the SCG, while Taylor’s stay in the middle was almost as short, lasting just two balls.
England were reeling when Joe Root (5) nicked off to Shane Watson in the slips and fell to 69-5 when Moeen Ali (22), who had swatted Starc for a 75-metre six, and Ravi Bopara (13) were caught out by Glenn Maxwell.
Morgan and Buttler (28), though, put on a measured 67 for the sixth wicket, with a sedate Buttler not scoring a boundary in his 60-ball knock, and Chris Woakes (8) combined with his captain to add 34.
Morgan continued to up the ante, bringing up three figures with a four-over cover, and found a useful ally in Chris Jordan (17), whose speedy running allowed the tourists to record an eighth-wicket stand of 56.
The England captain finally departed in the 48th over, pouched by Maxwell in the deep off Starc, and Starc then completed a four-wicket haul by shattering Steven Finn???s stumps as England were bowled out.