Hughes (112) and Bailey (89) batted together for the majority of the innings and set a great foundation for the Aussies to take a 1-nil lead in the five-match limited-overs series.
Hughes made history and became the first Australian to score a one-day international hundred on debut.
Australia finished with 5-305 after 50 overs with David Hussey on 60 and Brad Haddin 10.
No Sri Lankan bowler really made much of an impact the Australia batsmen, with all seven of the tourists bowlers going at over four an over.
Australian bowlers Mitchell Johnson, Clint McKay, Mitchell Starc and Xavier Doherty have a solid total to defend.
Hussey smashed 21 runs of the last over of the innings to set Sri Lanka a massive total to chase down.
Test aspirant Glenn Maxwell missed out on an opportunity to impress selectors after being caught by Ajantha Mendis off the bowling of Kulasekara.
Maxwell could only manage five runs from six deliveries but hit a spectacular boundary in his short stay at the crease.
Bailey missed out on becoming the second Australian centurion of the innings after he was dismissed for 89 off just 78 balls.
The stand-in skipper Bailey was aggressive from his first ball at the crease, punishing the Sri Lankan bowlers for eight boundaries and one six but all-rounder Angelo Mathews finally broke through.
After scoring his century, Hughes went on the attack and plundered 12 runs from a Lasith Malinga over before edging to wicketkeeper Dinesh Chandimal.
Hughes faced 129 balls and hit 14 boundaries in his innings.
Only seven players before Hughes have a made a century on debut in ODIs.
Hughes surpassed the highest score on debut for Australia which was Phil Jaques's 94 against South Africa.
Hughes and Bailey steadied the innings after losing Aaron Finch and Usman Khawaja in quick succession and have brought up their 100 partnership off 106 balls.
Batsman Phil Hughes becomes the first Australian to score a century on ODI debut - Getty Images
Bailey brought up his fourth ODI half century in a controlled innings from the Tasmanian.
He only needed 44 balls to bring up the milestone, hitting five boundaries and one six.
Debutant Khawaja was run out for just three off 11 balls after a sharp piece of fielding from Jeevan Mendis.
Khawaja looked extremely disappointed as he walked off the MCG, Khawaja called for a run but his partner Hughes sent him back and fell short of his crease.
Sri Lankan captain Mahela Jayawardene made the change to bring on Mendis and he broke through with the fifth ball of his first over.
Finch was trying to push forward, Mendis's delivery bounced a bit more than he expected and it took the edge and was taken by 'keeper Chandimal.
The three Australian debutants were given their ODI caps by former Aussie batting stars.
Former captain Mark Taylor presented to Finch, Dean Jones to Hughes and Michael Slater to Khawaja.
Michael Clarke's replacement, Bailey will be keen to shake the "Australian B-Team tag" with a win first up.
Queenslander Ben Cutting and all-rounder Steve Smith have been left out of the final XI.
The Sri Lankans are looking to bounce back from a disappointing 3-0 whitewash in the recent Test series, the tourists are renowned improved performers in the shorter forms of the game.
Sri Lanka: Tharanga, Dilshan, M.Jayawardene (c), Thirimanne, Mathews, Chandimal, J.Mendis, Perera, Kulasekera, Malinga, A.Mendis.
Australia: George Bailey (c), Xavier Doherty, Aaron Finch, Brad Haddin, Phil Hughes, David Hussey, Mitchell Johnson, Usman Khawaja, Glenn Maxwell, Clint Mckay, Mitchell Starc