Sri Lanka signalled that they are also in fine form for the knockout stages by having a good crack at what would have been a record run chase with Kumar Sangakkara becoming the first man to score three successive centuries at a World Cup.
They were always up against it after Maxwell's 53-ball 102 had helped Australia to 376-9, however, and it is the co-hosts who are now almost certain to finish second in Pool A and avoid champions India or South Africa in the quarter-finals.
On a night when the 40,000 crowd were thrilled by a feast of batting, it was Maxwell's deployment of the full array of shots in his prodigious armoury that proved decisive.
His hundred came off 51 balls, just one shy of the record for the quickest World Cup century, and he shared a 160-run partnership with Shane Watson, who hit 67 to celebrate his recall to the team.
Maxwell was dropped by a back-peddling Sangakkara on 95 and there was a nervous wait on 99, his chance of sharing the World Cup record with Irishman Kevin O'Brien disappearing when the umpire ruled a leg bye off the 50th ball he faced.
The century came up soon enough with two runs to mid-off, though, and his emotional celebration after reaching the milestone in his 43rd one-day innings was a graphic illustration of what it meant to a player often dismissed as a show-pony.
Steve Smith (72) and skipper Michael Clarke (68) had earlier steadied the innings with a partnership of 134 after openers David Warner (nine) and Aaron Finch (24) had been dismissed inside the first 10 overs.
Maxwell hit 10 fours and four sixes in his innings and the pyrotechnics continued when Sri Lanka came out to bat, Tillakaratne Dilshan setting the tone by spectacularly hitting six fours off Mitchell Johnson's third over.
Johnson had already dismissed Lahiru Thirimanne caught behind for one in his opening over to bring Dilshan and Sangakkara together at the crease.
While their 130-run partnership continued, it looked like Sri Lanka had a chance but once James Faulkner (3-48) trapped Dilshan in front for 62, it looked like an uphill struggle.
Sangakkara had already become only the second player after Sachin Tendulkar to score 14,000 runs in one-day internationals and was not going to be denied his century, which he reached in as many balls with two runs to backward square.
He departed soon afterwards for 104, leaving Dinesh Chandimal, who hit 52 off 24 balls before retiring hurt, and Angelo Mathews (35) to lead the rearguard action.
They were finally dismissed for 312 after 46.2 overs.
(Editing by Sudipto Ganguly)
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