Trailing 2-0 in the series, England needed a win in Mumbai to keep alive the series but the tourists now require something extraordinary to even save the match following Kohli's batting masterclass.
India piled on 631 in their first innings on the fourth day, a lead of 231 runs over England, after Kohli's third double century of the year.
The touring side were 182 for six in their second innings at stumps, still trailing by 49.
Kohli masterclass puts India in front
Jonny Bairstow was unbeaten on 50 with nightwatchman Jake Ball falling for two in the last over before the close.
Paceman Bhuvneshwar Kumar dismissed first-innings centurion Keaton Jennings for a golden duck and left-arm spinner Ravindra Jadeja sent back England captain Alastair Cook for 18 and Moeen Ali for naught to leave England tottering at 49-3 at tea.
Joe Root and Bairstow hit brisk fifties during their stand of 92 for the fourth wicket before the former fell leg before to off-spinner Jayant Yadav for 77.
The wickets of Ben Stokes, who made 18, and Ball to off-spinner Ravichandran Ashwin towards the end further dampened England's hopes of saving the match.
India wrest back control after England post 400
Bairstow was given out by umpire Bruce Oxenford first on 32 and then on 37 but the England wicketkeeper managed to overturn the decisions both times on review.
Earlier, the 28-year-old Kohli was out for a career-best 235 and added 241 for the eighth wicket, the highest for India, with Yadav, who scored 104, his maiden Test hundred.
Kohli, who was on 147 overnight, and Yadav continued to torment the England bowlers who went wicket-less in the first session after India resumed on 451 for seven.
Jennings scores debut ton as England make solid start in Mumbai Test
The right-handed batsman has now scored a double hundred in all three series India have played in 2016 — in West Indies, against New Zealand and now against England.
Published in The Express Tribune, December 12th, 2016.
Like Sports on Facebook, follow @ETribuneSports on Twitter to stay informed and join in the conversation.
COMMENTS
Comments are moderated and generally will be posted if they are on-topic and not abusive.
For more information, please see our Comments FAQ