Ballance, Morgan lead England to 269-7
England's Gary Ballance (front) runs between the wickets with teammate Eoin Morgan during the first ODI against Australia in Melbourne on Januray 12, 2014
Ballance, who came to the crease when England were struggling at 22-2, held the innings together before accelerating towards the end when quick runs were needed.
He shared in an 83-run partnership with Morgan, who blasted his 20th ODI half-century off just 47 balls with five fours and a towering six.
England had earlier won the toss, with skipper Alastair Cook having no hesitation in batting first on a flat MCG wicket.
But Cook's miserable tour of Australia continued when he fell for four, edging Clint McKay to wicketkeeper Brad Haddin.
McKay struck again to remove the equally out of form Joe Root, who was trapped in front leg before for three with the score on 22.
Ian Bell (41) tried to launch a rescue mission, hitting two fours and a six off Glenn Maxwell, but with the score on 62-2 he went for another heave over midwicket and was clean bowled by left arm spinner Xavier Doherty for 41.
That wicket brought Morgan to the crease and the Irishman played superbly, showing a confidence missing from the English Test players over the Ashes series.
However, he undid all his good work when, immediately after reaching his 50, he tried to hit Maxwell over cover, only to pick out Nathan Coulter-Nile to leave England at 145-4.
Some big hitting late in the innings from Jos Buttler (34) and Tim Bresnan (16) allowed England to reach a competitive total.