On a viciously turning track, England were shot out for 81 in the second innings, their lowest ever total against India, at the Narendra Modi Stadium.
Chasing 49 for victory in the spin-dominated, low-scoring contest, India overwhelmed the target without losing a wicket to go 2-1 up in the four-Test series.
The hosts need a draw in the final Test, also in Ahmedabad from March 4, to reach the WTC final against New Zealand.
England had been on the back foot since being skittled out for 112 in their first innings on a turning track at the world's largest cricket stadium.
Joe Root and Jack Leach shone with the ball to drag the tourists back into the contest by bowling out India for 145.
The tourists, however, suffered a second batting collapse to allow the hosts to take charge again.
Earlier, resuming on 99-3, India looked on course for a handy first-innings lead but Root (5-8) and Leach (4-54) wreaked havoc with the pink ball.
Rohit Sharma top scored for India with 66 but the hosts lost their last seven wickets for 31 runs.
Patel had claimed six of the 10 English wickets in the first innings and the left-arm spinner returned to haunt them with a two-wicket first over.
Ben Stokes (25) and Root (19) offered hints of a partnership before they fell in successive overs.
Patel went on to claim 5-32, while Ravichandran Ashwin dismissed four batsmen en route to reaching 400 Test wickets.
England lasted 30.4 overs with all 10 batsmen falling to spin.
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