Sri Lanka's batting had been insipid until now, but they finally posted a competitive score of 142 for six, with Kusal Perera hitting 57.
However their bowlers, led by Lasith Malinga, have been no match for a quality Australian batting line-up, spearheaded by Warner who has now scored 217 in three innings without losing his wicket.
"It was pretty clinical once we got into a routine," said Australia captain Aaron Finch. "The way the bowlers set it up for us over the last two games, it was outstanding. "Every game is a different challenge and a different surface, so it's important to bring in your best, in terms of preparation and mental side of the game too."
Openers Finch and Warner were both dropped early in the run chase at the Melbourne Cricket Ground, and they made the visitors pay, putting on 69 for the first wicket.
Finch hit three big sixes before falling for 37, caught by Shehan Jayasuriya off Lahiru Kumara.
That brought Steve Smith to the crease, but he only lasted nine balls, caught in the deep for 13.
Warner, who scored an unbeaten 100 and 60 not out in the opening two games, was heard on the pitch microphone saying he was struggling with his rhythm. But he still produced the goods, bringing up his 50 off 44 balls to end the match unbeaten on 57, aided by Ashton Turner who chipped in with 22 as Australia reached 145 for three with 14 balls to spare.
Australia have set a target of being the number one T20 side by the time the World Cup is played on home soil in a year's time, and their whitewash of Sri Lanka is set to propel them above South Africa and into third place.
An even bigger test starts on Sunday, when they face top-ranked Pakistan in the first of three T20s.
"We haven't been up to our standards. We haven't performed at our best and if we don't, we will end up like this," said Sri Lanka opener Niroshan Dickwella. "We learnt a lot in this series, but we couldn't even compete properly."
Finch won the toss and put Sri Lanka into bat and it didn't start well for the visitors.
Dickwella, elevated to opener after Danushka Gunathilaka was dropped, was out first ball.
Kusal Mendis and Perera showed some aggression, slapping a handful of boundaries, before Kane Richardson tempted Mendis into another big shot and he was caught at deep square for 13.
Scoreboard
========================================================== Sri Lanka ========================================================== K. Mendis c McDermott b Richardson 13 N. Dickwella c McDermott b Starc 0 K. Perera c Turner b Cummins 57 A. Fernando c McDermott b Cummins 20 O. Fernando c Carey b Richardson 6 B. Rajapaksa not out 17 S. Jayasuriya b Starc 12 L. Malinga not out 8 Extras: (lb8, w1) 9 ========================================================== Total: (six wkts, 20 overs) 142 ==========================================================
Did not bat: Lakshan Sandakan, Nuwan Pradeep, Lahiru Kumara
Fall of wickets: 1-3 (Dickwella), 2-33 (Mendis), 3-76 (A. Fernando), 4-99 (O. Fernando), 5-110 (Perera), 6-132 (Jayasuriya)
Bowling: Starc 4-0-32-2, Richardson 4-0-25-2, Cummins 4-0-23-2, Zampa 4-0-30-0, Agar 4-0-24-0
========================================================== Australia ========================================================== A. Finch c Jayasuriya b Kumara 37 D. Warner not out 57 S. Smith c Sandakan b Pradeep 13 B. McDermott lbw Malinga 5 A. Turner not out 22 Extras: (lb5, w6) 11 ========================================================== Total: (3 wkts, 17.4 overs) 145 ==========================================================
Did not bat: Alex Carey, Ashton Agar, Pat Cummins, Mitchell Starc, Kane Richardson, Adam Zampa
Fall of wickets: 1-69 (Finch), 2-85 (Smith), 3-99 (McDermott)
Bowling: Malinga 4-0-22-1, Kumara 4-0-49-1, Pradeep 3.4-0-20-1, Jayasuriya 2-0-24-0, Sandakan 4-0-25-0
Result: Australia won by seven wickets
Toss: Australia
Umpires: Shawn Craig (AUS) and Paul Wilson (AUS)
TV Umpire: Gerard Abood (AUS)
Match Referee: Javagal Srinath (IND).