England, set a challenging target of 172, slumped to 103 all out inside 17 overs, wrist spinner Kuldeep finishing with figures of 3-19 and the orthodox Patel 3-23.
India, bidding for their first major title since the 2013 Champions Trophy, will now play South Africa - also unbeaten at this tournament after a nine-wicket hammering of Afghanistan in their semi-final - in Saturday's final in Barbados.
The Kensington Oval clash will also be India's second appearance in successive global showpiece games after they lost on home soil to Australia in last year's 50-over World Cup final.
England captain Jos Buttler launched the title-holders' chase with a brisk 23. When he attempted to reverse sweep Patel's first ball, however, he clipped a gentle catch off the toe-end of the bat to wicketkeeper Rishabh Pant.
Fellow opener Phil Salt was then clean bowled by Jasprit Bumrah's well-disguised slower ball.
India had had their problems on a slow surface while making 171-7 but, even before the tournament started, they knew they would play a semi-final on a Providence pitch renowned for aiding spinners if they got through to the last four.
England then saw 34-2 become 35-3 when Patel bowled dangerman Jonny Bairstow for a duck.
Moeen Ali was then stumped by Pant and when Sam Curran was lbw to Kuldeep, England were in dire straits at 49-5 in the ninth over.
Harry Brook threatened to lead a recovery before he was bowled by Kuldeep for 25.
The last thing England needed now as a run-out but that was exactly what they got as Liam Livingstone (11) was left stranded after a dreadful mix-up with Jofra Archer to leave the champions all but beaten at 86-8 off 15 overs.
Archer struck a couple of defiant sixes but Bumrah ended the match when he had the England paceman lbw for 21 with a low full toss.
Earlier, India captain Rohit Sharma hit his third fifty of the tournament in a total of 171-7 after Buttler won the toss.
India were 40-2 in the powerplay after Virat Kohli (nine) and Rishabh Pant (four) both fell cheaply.
But a third-wicket partnership of 73 between Rohit (57) and Suryakumar Yadav (47), spanning a rain delay of over an hour, turned the tide.
Kohli's miserable tournament with the bat continued when he was bowled by left-arm quick Reece Topley.
But England, who overpowered India by 10 wickets in the 2022 semi-final in Adelaide, had another success when Pant chipped Curran to midwicket.
India were 65-2 off eight overs when rain stopped play, with Rohit 37 not out and Suryakumar unbeaten on 13.
When play resumed, Rohit fresh from his blistering 92 against Australia, smashed spinner Livingstone for six over long-on and, on one knee, swept Curran for another remarkable six to complete a 36-ball fifty.
But with Rohit threatening to cut loose, leg-spinner Adil Rashid bowled him with a googly before Suryakumar holed out off fast bowler Archer.
