Saturday's (Sunday AEST) win, with 62 balls to spare, was a 15th in a row for England over Sri Lanka in the format and takes Harry Brook's side back to No.1.
Chasing a modest 125, after Sri Lanka collapsed to 124 all out with seven balls remaining, the hosts were 1-22 after opener Aneurin Donald was stumped for 13 but Buttler and Brook then stepped up to take control, ending the six-over powerplay at 1-82.
Buttler, who on Thursday became the first batsman to reach 15,000 career T20 runs, brought up his half-century with a six and sent England to a winning 2-126 with another as he made a top-scoring 62 from 32 deliveries while Brook contributed 33 before being run out.
Brook ended as top overall scorer and player of the series.
""I think we should be extremely proud to win another series, another whitewash, and to go back to world number one," he said.
"It's an extremely good effort and everyone in the changing room should be really proud of themselves.
"We obviously knew we had the opportunity to go to number one before this series, if we were to beat them 3-0, and that was always in the back of our minds. The opportunity of whitewashing a side is something you never want to take for granted."
England, unchanged from the side that won the second T20 by six wickets in Cardiff on Thursday, again won the toss and opted to bowl as they chased the sweep, with a strong breeze blowing at Old Trafford.
Will Jacks, Jofra Archer and Player of the Match Sonny Baker took two wickets each as Sri Lanka faded after ending their powerplay at 2-47.
Opener Pathum Nissanka (36 off 24) top-scored for the visitors before being caught by Brook off Jacks while Kamindu Mendis was caught by Jacks off Archer for 35 from 28 balls.
Wanindu Hasaranga (seven from six) knocked a bail off his own wicket after taking a hefty swing at an Archer delivery and tail-ender Eshan Malinga was run out for a duck by Liam Dawson while seeking a single.
Captain Charith Asalanka was needlessly run out for 16 as Sri Lanka slumped to 4-83.
England play three one-day internationals against Sri Lanka next week, starting at Durham's Chester-le-Street ground on Tuesday with matches at Leeds' Headingley on Thursday and London's Oval on Sunday
