Wing Kenki Fukuoka led the way with two tries, while Kotaro Matsushima and Keita Inagaki also scored as the hosts held off a fierce second-half assault from a team they had lost against in all seven of their previous meetings.
When Japan beat South Africa four years ago - having won only one of their previous 24 World Cup matches - it was considered the greatest shock in rugby history. This time, having already beaten Ireland three weeks ago, it did not even feel like a real surprise.
They were faster, sharper, more inventive and, roared on by the vast majority of the delirious red-and-white-clad crowd, absolutely relentless in everything they did as they became the first tier-two team to reach the last eight since Fiji in 2007.
Having won all four of their matches to top Pool A with 19 points, they will face the Springboks again in the quarter-finals and the twice-champions will be taking absolutely nothing for granted.
The result also meant that Ireland, through as runners-up on 16 points, will play New Zealand.
"Tonight we went another level," said Japan coach Jamie Joseph. "They wanted it as much as the Scots and gave as much as they could. This is what it takes to win big test matches."
The match was given the go-ahead only on Sunday morning after an inspection of the damage caused by Typhoon Hagibis and proved a wonderfully uplifting occasion for the country after the death and destruction wrought by the storm.
"Whilst we are celebrating tonight there are a lot of people who aren't," Joseph said.
Captain Michael Leitch said that the victory owed more to heart than skill and while that might be true of their mighty defensive effort in the final quarter, no team in the tournament so far has come close to matching the pace and directness of Japan's first-half assault.
EXPLOSION OF NOISE
Scotland were first on the board with a Finn Russell try after seven minutes but Japan hit back with a brilliantly-worked, high-tempo score that set the tone for the night as Fukuoka tore clear and slung a one-armed pass into the arms of the supporting Matsushima to detonate an explosion of noise.
Japan were playing with a speed and intensity that the Scots just could not live with and got a third try at the end of the half when Tim Lafaele slipped through a deft grubber that bounced perfectly into the arms of Fukuoka.
It was then bedlam two minutes into the second half when Fukuoka stripped Chris Harris and galloped clear for a fourth and bonus-point clinching try.
The Scots, who came from 31-0 down to draw 38-38 with England in the Six Nations in March, channelled that Twickenham spirit as WP Nel and Zander Fagerson scored to get back within seven points with 25 minutes to go but with the bonus-point situation, they still needed more than two converted tries to advance.
It was relentless Scottish pressure and desperate, at times demented, Japanese defending from then on, but the hosts held out for another famous victory in what became a deafening cauldron of noise.
It was only the second time Scotland have failed to reach the last eight - the other coming in 2011 - but they can have few complaints, bookending wins over Russia and Samoa with defeats by Ireland and the hosts. "We had a mountain to climb after that first half but we started climbing it and I thought the effort the players put in to get back to within seven points was excellent," said Scotland coach Gregor Townsend. "We were obviously aware that this was huge for the home nation. The atmosphere was absolutely fantastic and you didn't want to be the team that was losing in that atmosphere."
