Buttler's late onslaught at the end of the England innings, alongside Chris Woakes, who finished 53 not out, saw the tourists post an imposing 302-6 from their 50 overs after being sent in to bat first.
The Aussies were always in the game in the reply but when batsmen were set at the crease they never went on to get the big score, which saw the hosts finish 16 runs short in the chase on 286-6 from their 50 overs.
Smith calls toss as Aussies apply pressure
Steve Smith finally won the toss for the first time in the series and chose to bowl first in a game that the Aussies had to win to stay in the series.
England openers Jonny Bairstow and Jason Roy got off to a flying start with the bat but their partnership was broken for 38 when Pat Cummins removed Roy for 19.
Not long after getting the first wicket, the Aussies got a second when Alex Hales fell for one off the bowling off Marcus Stoinis.
The fall of the Hales' wicket saw Joe Root come to the crease and alongside Bairstow the pair tried to steady the ship and set up a good platform for the rest of the innings.
It was working well until Adam Zampa bowled Bairstow for 39 to reduce the tourists to 90-3.
Root then fell for 27, 17 runs later, as Josh Hazlewood became the first bowler to dismiss the England batsmen in the series.
Morgan stands tall
The tourists needed Eoin Morgan to stand up and alongside Buttler, the pair put on a half-century partnership for the fifth wicket.
Just as the partnership was looking very dangerous for the Aussies, Hazlewood came back into the attack and removed Morgan for 41.
Moeen Ali again struggled with the bat and fell for six off the bowling off Mitchell Marsh leaving England on 189-6.
Buttler and Woakes fireworks
England, therefore, needed some big hitting in the last ten overs of the innings to get up to a competitive score and that is exactly what happened.
Buttler and Woakes together hit 102 runs from the final ten overs of the game to get England up and past 300.
During the partnership, Woakes hit a half-century of 35 balls, while Buttler smashed his way to a brilliant century as England finished on 302-6 from their 50 overs.
Finch again talisman for hosts
In reply, David Warner once again fell cheaply for eight off the bowling off Woakes much to the joy of the England bowlers,
Cameron White didn't last much longer for the Aussies as he fell for 17 off the bowling of Mark Wood.
Aaron Finch though was still at the crease and once again he passed a half century after scoring hundreds in the first two games of the series.
Alongside, Smith, Finch also put on a half-century partnership with his captain before playing one big shot too many as he was trapped LBW by Adil Rashid for 62.
Smith, though, now joined by Marsh at the crease, looked like he was going to go on and get a big score as the pair put on 68 for the fourth wicket.
Smith given out in controversial fashion
The partnership was broken in controversial fashion as Wood found Smith's edge which went low to Buttler, who claimed the catch, and after much deliberation the third umpire said that it was out much to the anger of Smith, who thought the ball hit the ground.
Marsh now joined at the crease by Stoinis, passed his half century and looked good until he mistimed a shot off the bowling off Rashid to fall for 55.
Paine and Stoinis fall short
It meant that Tim Paine and Stoinis had work to do to win the game for the hosts and they looked like they were going to see the Aussies home as Stoinis passed a half-century and looked in the mood to keep going.
Good tight bowling from the tourists though meant that the Aussies needed 24 runs from the final over to win the game.
Stoinis fell for 56 with three balls remaining off the bowling off Woakes however, as the Aussies fell 16 runs short with the bat as the tourists sealed the series with two games to play as Paine finished 31 not out.
After Ashes humiliation during the course of the last few months, England take an unassailable 3-0 advantage to the Adelaide Oval on Friday, before the fifth ODI at the new Perth Stadium, as the visitors now themselves eye a famous series whitewash.