Sanju Samson, match-winnner in their do-or-die win over the West Indies, fired once again to crash 89 off 42 balls and lead India to 7-253, the fourth-highest total in the tournament's history, on Thursday (Friday AEDT).
Faced with a record-breaking chase, Bethell then kept Mumbai's Wankhede Stadium quiet for long periods as he plundered a 48-ball 105 to keep England dreaming.
But consummate death bowling from Jasprit Bumrah and Hardik Pandya proved too much as England fell short on 7-246 and the champions set up a final on Sunday (Monday AEDT) against New Zealand in Ahmedabad where they can become the first team to successfully defend the title.
Amid a batting paradise at Indian cricket's spiritual home, a feast of 499 runs, featuring 34 sixes — 19 by India and 15 from England -- was served up.
But, ultimately, a couple of moments of brilliance - and one butterfingered episode - made all the difference.
The butterfingers belonged to England captain Harry Brook, who dropped a dolly of a catch at mid-on in just the third over off Jofra Archer's bowling that spared Samson on 15.
"I made a big mistake," sighed the skipper, who'd put the Indians in and would have had them reeling at 2-24.
Instead, Samson went on to crack eight fours and seven sixes, while his teammates flew along at a similar pace, with Ishan Kishan (39 off 18 balls), Shivam Dube (43 off 25), Hardik Pandya (27 off 12) and Tilak Varma (21 off seven) all motoring on at rates over 170.
Brilliance then brought the downfall of England's key man Brook, who sliced a fantastic slower ball from Bumrah over the covers and Axar Patel ran back 25 metres to to take a wonderful sprawling catch.
Having to play hit-or-bust cricket, England had slumped to 4-95, but their man of the tournament Will Jacks (35 off 20) combined with Bethell to put on 77 in just over six overs and start to unnerve India.
Once again, Patel made an astonishing contribution in the field, catching Jacks' shot over deep cover on the boundary edge while off balance but still having the presence of mind to flick it to fellow fielder Dube before toppling over the ropes.
With eight fours and seven sixes, Bethell then became only the fourth England batter after Jos Buttler, Dawid Malan and Brook to make a century in all three international formats with his remarkable century.
"Bethell was absolutely unbelievable, he's going to have a hell of a career with England, he showed the world how good he was tonight," said Brook.
But Bumrah (1-33) delivered a killer 18th over, conceding only six runs, which put too much pressure on the left-hander.
Bethell still managed to hit Pandya for six to bring up his ton in an otherwise tight penultimate over but was run out by the allrounder at the start of the final over when 30 were needed and he was trying desperately to complete a second run to keep the strike.
Bumrah was the difference, not for the first time. "All credit goes to him," Samson said as he collected the man-of-the-match award.
"The world-class, once-in-a-generation bowler, that's what he delivered today. This award should go to him actually."
Archer, whose 1-61 were the most expensive figures in England's history at the tournament, hit three consolation sixes in that final over off Dube but it was too little too late.
