Ravi Ashwin was the star of the show as a late treble with the ball added to his earlier 72 runs as he put his side in a strong position going into the fourth day.
Ravindra Jadeja (90) also contributed as India finished with a first innings lead of 134 to put the tourists under real pressure.
Ben Stokes took 5-78 and Adil Rashid 4-138 to offer England a glimmer of hope going into the business end of the game.
India started the day trailing by 12 runs with their score on 271-6.
The strong partnership late on day two from Ashwin and Jadeja meant the hosts began Monday morning firmly in the ascendancy.
The partnership continued in the same manner early on and a quick 30 meant India gained the first innings lead and pushed the overall score above the 300 mark.
It was Stokes who broke the stand when he tempted Ashwin (72) into an uppish drive in his first over, the Indian all-rounder finding Jos Buttler at backward point.
Jadeja, however, continued to march on and he brought up his third half-century in Test cricket shortly afterwards.
The frustrating partnership of Jadeja and Jayant Yadav proved to be a tough act to break for England as the pair pushed the lead beyond 70 and into the lunch break at 354-7.
A flurry of boundary hitting, including four in one Chris Woakes over continued to put England to the sword.
Jadeja was the man who did the damage and found himself 90* from 167 balls. He, however, wouldn’t make his first test century and lost his wicket shortly afterwards.
Rashid entered the attack and with his first ball tempted Jadeja into a big shot, caught at long on by Woakes to leave India 381-8.
Umesh Yadav brought up India’s 400 with a towering six off the bowling of Moeen Ali before the other Yadav, Jayant, brought up his first half-century with a pushed single off Stokes the very next over.
Stokes picked up his fourth wicket of the innings to dismiss Jayant for 55 and soon had his third five-wicket haul in Test cricket, Umesh caught behind and the hosts all out for 417, a lead of 134.
The tourists, began their second innings with a new opening partnership after Haseeb Hameed was deemed not fit enough to bat at the top of the order after injuring his finger in the first innings.
Alastair Cook was living dangerously early on and survived two LBW reviews in the space of two balls from Jadeja.
Cook (12) did go on to lose his wicket though when a smart delivery from earlier batting hero, Ashwin, beat his defences.
The restructured batting line-up saw Moeen Ali come in number three.
The Worcestershire all-rounder, however, failed to contribute significantly and fell when miscued a delivery from Ashwin and found the waiting hands of Jayant Yadav.
A short resistance from Root and Bairstow stopped the flow, but Bairstow (15) lost his wicket when he nicked behind off Jayant to leave England 70-3.
Ashwin then got the key wicket of Stokes, trapped LBW on review, as England were left teetering on 78-4 at the end of day three in Mohali.
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