In ICC T20I Team Rankings, Australia moved from 110 to 114 points to go past England, which has slipped from 116 to 113 after its loss to Pakistan in the one-off T20I.
Sri Lanka fought back after Maxwell's belligerent knock, but the visitors got across the line with 13-ball to spare.
The 27-year-old batsman hammered an unbeaten 65-ball 145 to help the visitors post the highest total taken a 1-0 lead.
Dinesh Chandimal will captain Sri Lanka in their Twenty20 series against Australia.
Australia batsmen Aaron Finch and Chris Lynn have been ruled out of the two-match Twenty20 series in Sri Lanka with injuries.
Australia clinched the series 4-1 after as they defeated Sri Lanka by 5 wickets thanks to David Warner's knock of 106.
Aaron Finch blitzed an 18-ball half-century as Australia chased down 213 with 19 overs to spare, takes an unassailable 3-1 lead.
Half-centurion George Bailey starred in Australia's tense run chase as the visitors edged past Sri Lanka by two wickets in the third one-day international and took a 2-1 lead in Dambulla on Sunday.
Vice-captain David Warner will lead the side for the remaining three one-day internationals and two Twenty20 matches against Sri Lanka.
Amila Aponso picked career best four wickets, despite Faulkner hat-trick as SL beat Australia by 82-run, level 5-match series 1-1.