Batting first, Sri Lanka kept losing wickets at regular intervals to struggle once again with the bat.
The Aussie bowlers worked well as an unit with Adam Zampa (2/20) leading the show.
Kusal Perera (27) was the top run-scorer for Lanka.
In reply, Australia lost skipper Aaron FInch for a first-ball duck.
However, Warner and Smith stitched an unbeaten century-plus stand to help Australia.
David Warner in a league of his own
Warner, who amassed an unbeaten 100 in the first T20I, registered another superb knock.
The southpaw surpassed the 1,900-run mark for Australia in T20Is (1,952).
He needs just 48 more to get to the 2,000-run mark and be the first Aussie to do so.
Warner also notched his 14th career T20I fifty.
He is nine boundaries away from registering 200 fours (191).
Smith notches third career T20I fifty
Smith, who made a return to T20Is after more than three years. hit his third career T20I fifty in his 32nd match. This was his maiden fifty against Sri Lanka in the shortest format. His last fifty (61*) came against Pakistan in 2016 at Mohali.
Warner-Smith notch record-breaking stand
Smith shared a 117-run stand for the second wicket alongside Warner.
This is Australia's best stand for the second wicket in T20Is.
Their previous best was 114 against England in 2013.
This was also their seventh-best stand for any wicket in T20Is.
The 117-run stand is also the second-best for any wicket against Sri Lanka in T20Is.
Australia win maiden T20I series at home against Lanka
This was Australia's maiden T20I series win against Sri Lanka at home.
Prior to this, Lankans had won three T20I series on Australian soil.
Australia also sealed a second successive T20I series this year.
They have a 4-0 record in 2019.
Australia registered their seventh win against Sri Lanka in T20Is.
Finch notches fourth career T20I duck, Malinga gets 105th scalp
Aaron Finch recorded his fourth career T20I duck. He equaled former Australian cricketer David Hussey with this unwanted record. Lasith Malinga (1/23) raced to 105 career T20I wickets.