After Buttler top-scored with 61 in a total of 264 for eight, a brittle home batting line-up was sprung out for 92 in 26 overs on a stifling day in Canberra and in front of Australia Prime Minister Tony Abbott.
Ravi Bopara completed a quick kill as he claimed four wickets in 17 balls, for the cost of three runs, as England won for the first time since their only other success on tour, against a Cricket Australia Invitational XI in Sydney.
"It's great to get a win," Buttler said.
"It's going to be a morale-boost for everyone, no matter who it is against."
While overcoming Australia still remains on the to-do list, Cook's men will at least take positive thoughts to Brisbane for Friday's second one-day international.
"There were a lot of positives that came out of today," Buttler added.
"We got up to a challenging total and put them under pressure straight away with the ball. We had a lot of energy and we really tried to target early wickets and we got those.
"Everyone is pleased to get a win and hopefully we can take that momentum forward to Brisbane."
England's team selection reflected an intent to end their losing run after naming a near full-strength XI, with Michael Carberry and James Tredwell the two changes from Sunday's six-wicket defeat to Australia in the opening ODI.
Carberry pressed his claims for a place in Brisbane with a fluent 47 from 50 balls - while skipper Alastair Cook and Joe Root both failed with the bat again.
The English pair succumbed to a fiery initial burst from 37-year-old former Australia quick Brett Lee, which accounted for Cook in the first over for the second successive game.
The skipper was drawn into a nervous push at a short ball and Root likewise had managed just one run, from 14 balls, before getting a rough lbw call.
It meant Carberry was freed to make his case for a call-up to a faltering top-order and did so in a 75-run stand with Gary Ballance (56) - who registered a second successive half-century.
England still needed another significant partnership after slipping to 149 for six in the 30th over - Buttler and Tim Bresnan (36) obliged as they put on 80.
Buttler was particularly impressive, given a rare chance to build an innings in England colours, and intelligently used the wide expanses of a slow Manuka Oval outfield to keep the score ticking.
Regularly a big hitter, he found the ropes just four times in a run-a-ball century. Given England's problems at the top of the order, it was the type of batsmanship to suggest he could be elevated and also provide the firepower that has been missing in the two 50-over matches so far.
Buttler does not believe that is on the agenda of coach Ashley Giles or Cook just now, though.
"That's down to the management and the captain as to what they see is best," he said.
"I'll bat anywhere. Number seven is where I've been playing in one-day cricket since I've been playing in this side and I don't see that changing.
"That's what everyone wants to do - bat as long as they can.
"I'll bat wherever. I'm not fussed."
England opted not to select Steven Finn - the only quick not to play during the Ashes - and Lee admitted he was "shocked" by the decision.
Lee regards Finn as a major prospect for the future, but the 24-year-old has seemingly regressed on this tour.
"I've been shocked he hasn't been playing," he said.
"Going back a few years ago playing against him he's a quality bowler. I know they are not saying he's not a quality bowler but he's not been given the opportunity.
"I can comment on this because I was on the sidelines for 18 months in Test cricket. You've just got to be ready to go.
"I know it can be very tough to bowl in the nets day in, day out.
"It's completely different when you go out there and it will be tough for him to go out there and hit his areas straight up.
"I hope for his sake he gets a run (during the one-day series)."