England, the 2019 champions, stayed last with two points and only one win in six games. Australia in 1992 is the only other defending champion to lose four or more matches at a World Cup.
Chasing 230, England faltered after their openers put on 30 runs.
Bumrah bowled Dawid Malan in the fifth over for 16. The very next ball, Joe Root was out lbw for a golden duck – plumb in front, shuffling across the stumps. He appealed unsuccessfully.
While Bumrah’s hat trick was denied, Shami then was on one himself at the other end. His opening overs were near unplayable as Ben Stokes struggled to put bat to ball.
Stokes went for a slog and was bowled in the eighth over for a 10-ball duck. The very first ball of his next over, Bairstow played on off Shami as England was down to 39-4 in 9.1 overs.
The pacers’ opening salvo saw England lose four wickets for nine runs across 26 balls.
After a drinks break, it was spin’s turn. Despite heavy dew, Kuldeep Yadav sent down a beauty to bowl Jos Buttler for 10. Buttler had no clue as the ball turned in sharply off length, leaving England at 52-5.
Moeen Ali and Liam Livingstone added 29 runs for the sixth wicket – the second highest partnership of England’s innings. But the pressure never eased.
Shami returned to have Ali caught behind for 15 runs and Ravindra Jadeja had Chris Woakes stumped for 10 in the 29th over.
Yadav then trapped Livingstone lbw – out for 27 – as England crashed to 98-8.
England did manage to reach 100 but it was small consolation as Shami-Bumrah returned to finish off proceedings.
Earlier, India got off to a poor start as England choked the top-order. Woakes bowled Shubman Gill for nine in the fourth over and three overs later, India was 27-2 as Virat Kohli chipped to mid-on and was out caught for a nine-ball duck off David Willey.
Woakes sent back Shreyas Iyer for four runs, out caught pulling a short ball, his Achilles’ heel as the score read 40-3 in 11.5 overs.
Sharma and Lokesh Rahul resisted with a sedate 91-run partnership for the fourth wicket in their 111-ball partnership.
The usually hard-hitting Sharma played an innings of great control. He did survive an lbw shout early on, but the ball was gliding past leg stump on DRS review.
Sharma scored his second half-century in the tournament – his fifth 40-plus score in six innings – off 66 balls as he anchored the Indian innings.
At the other end, Rahul scored 39 off 58, with three fours, but fell against the run of play. Willey returned to dismiss him in the 31st, as Rahul mistimed a pull shot.
Wrist spinner Adil Rashid bowled with great control for England, taking 2-35 in 10 overs. His first wicket was vital to hold back India’s score – Sharma holed out to deep midwicket, 13 runs shy of his hundred.
At 164-5, India was in trouble and England looked in control. Suryakumar Yadav helped push the score past 200.
Yadav scored 49 off 47 balls, with four fours and a six. He put on 18 runs with Jadeja (18), and then another 25 with Bumrah.
Yadav was caught off Willey, leaving India at 208-8. Bumrah and Kuldeep Yadav added 21 runs for the ninth wicket.
England has only beaten Bangladesh and has also lost to New Zealand, Afghanistan, South Africa and Sri Lanka.
Star all-rounder Hardik Pandya was still unavailable for India and is nursing a left ankle injury. In his absence, the hosts went with a similar combination as it did against New Zealand a week ago in Dharamsala – six batters and five bowlers.
Both India and England fielded an unchanged side at the BRABVE Stadium.