Chasing a winning target of 289, tournament co-host India were on course for victory for much of their innings on Sunday.
Smriti Mandhana top-scored with 88, while captain Harmanpreet Kaur hit a run-a-ball 70.
England captain Nat Sciver-Brunt picked up 2-47 in eight overs, while left-arm spinner Linsey Smith bowled a tight spell - 1-40 in 10 overs, including Mandhana's vital wicket - as England applied the brakes to pull off a stunning win.
India finished with 6-284 in 50 overs in front of a shocked home crowd at the Holkar Stadium. It was their third straight loss in the tournament.
It all came after England had opted to bat and put on 8-288 in their 50 overs, thanks to Heather Knight's 109 off 91 balls.
Player of the match Knight, who was playing her 300th international, said: "I got myself in and put down the accelerator. It felt like we needed 300 on that pitch but it was frustrating to not get there in the end.
"I was desperate to put in a statement performance for my 300th and I am pleased to do that."
England have joined defending champions Australia and South Africa in the semi-finals with a fourth win in five games. They are unbeaten in the tournament and climbed to second place in the points table.
The four-time champions next play leaders Australia on Wednesday at the same venue.
India remain fourth with four points from five games but now need a massive turn-around in form against New Zealand (Thursday) and Bangladesh (Sunday) in their final two games at Navi Mumbai.
Co-host Sri Lanka take on Bangladesh, also at Navi Mumbai, on Monday.
The semi-finals will be played on October 29 and 30, with the final on November 2.
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