The Aussies bowled well to limit the visitors to 142.
In reply, Australia rode on a superb 69-run opening stand to set up the chase.
Warner was terrific with an unbeaten 57.
Australia enjoyed a famous win.
Warner surpasses 2,000 career T20I runs, stays unbeaten in series
Warner became the first Australian cricketer to surpass the 2,000-run mark in T20Is (2,009).
He became the sixth batsman in the world to achieve this remarkable feat.
The southpaw amassed his 15th career T20I fifty.
He now has 195 fours and 84 sixes in T20Is.
Warner ended up with 217 runs in the series and scored three successive unbeaten fifty-plus scores.
Finch surpasses Watson, notches this feat with Warner
Aaron Finch (37) hit one four and three sixes in the match.
He surpassed former Aussie great Shane Watson (83) in terms of career T20I sixes (85).
He also raced to 1,772 career T20I runs.
The Aussie skipper added another fifty-plus stand alongside Warner atop.
This was their second fifty-run stand in T20Is.
They have now amassed 572 partnership runs in T20Is.
Perera slams 11th career T20I fifty, Malinga impresses
Kusal Perera notched his 11th career T20I fifty.
He now has 1,171 runs in the format.
Perera slammed one six in the match and increased his tally to 41 in T20Is.
Veteran fast bowler Lasith Malinga (1/22) raced to 106 career T20I scalps.
He now has 12 wickets against the Aussies in T20Is.
Starc scripts a special feat, Aussies maintain 100% record
Mitchell Starc (2/32) is now the fifth-highest T20I wicket-taker for Australia (35). He went past Nathan Coulter-Nile (34). Pat Cummins (2/23) now has 31 career T20I scalps. Australia now have a 5-0 record in 2019. They registered their eighth win against Sri Lanka in T20Is.