England were viewed as marginal underdogs and the absences of Mark Wood and Dawid Malan due to injury increased the sense of foreboding, but they made a mockery of pre-match predictions.
While Hardik Pandya's buccaneering 63 off 33 balls helped India add 88 in the last seven overs to post 168 for six, his efforts were put in the shade by the belligerence of Buttler and Alex Hales.
The pair's unbroken 170-run stand set a new benchmark for the highest partnership for England's opening wicket, with the pair sharing 13 fours and 10 sixes to secure a scarcely-believable 10-wicket win with four overs to spare and set up a showdown against Pakistan at the MCG on Sunday.
"I'm immensely proud of the guys, that was a brilliant performance, by far our best performance of the tournament," said Buttler, whose side stuttered rather than stormed into the knockout stages.
"We're a good team, I think that's probably where the performance comes from. We've got some brilliant players in our team and when they play their best, they're a tough team to beat.
"We're an incredibly dangerous side, there's huge confidence in the group, we haven't at points played as well as we could have done in the tournament yet still found ourselves in the semi-final of a World Cup.
"To play like we did in such a high-pressure game is immensely satisfying."
Hales capitalised on the shorter square boundaries at the Adelaide Oval in front of a largely pro-Indian crowd of 40,094, setting a lung-bursting tempo that even Buttler struggled to keep up with, bringing up his 50 off 28 balls.
Buttler finished on 80 not out off 49 balls, smacking the winning runs with a six off Mohammed Shami, while Hales was unbeaten on 86 off 47 deliveries in a jaw-dropping union.
Hales had three and a half years in international exile, banished since a positive recreational drugs test on the eve of the 2019 50-over World Cup before being recalled in September, but he has had an impact in each of England's last three matches - all must-wins.
"He's delivered in spades," said Buttler. "He's immensely tough to bowl at, it was fantastic to be at the other end and watch him go about his business with such a wide range of shots.
"The dimensions of the ground, he played them fantastically well. A huge strength of his is square of the wicket which obviously on this kind of ground is really great."
Chris Jordan, who came in for Wood, took three for 43 while Adil Rashid leaked just 20 and collected the key wicket of the in-form Suryakumar Yadav, helping to stifle India in the middle overs which Buttler felt was crucial.
"The bowlers were outstanding," said Buttler. "I thought Adil Rashid had his best day for a while. He was so tough to play. I thought he looked like getting a wicket every over.
"A special mention to Chris Jordan to come into such a high-pressure game having not played in the tournament, I asked a huge amount of him to bowl three overs straight through at the death. It's a hell of a performance from Chris."
England have spoiled hopes of a mouth-watering India-Pakistan marquee contest but there will instead be a rematch of the 1992 50-over World Cup final, which Pakistan won.
England are one win away from unifying the ODI and T20 World Cups but Buttler insisted they will not be getting carried away with what they achieved on Thursday night.
"It's important we enjoy the performance but of course don't get too far ahead of ourselves," added Buttler. "The biggest game of this tournament is still to come.
"It's going to be an amazing occasion. You don't come down this road very often so it's certainly something to be relished."