The hosts declared on 710-7 and would have hoped to have made more runs were it not for stoppages for rain and bad light, while the loss of Virender Sehwag for a golden duck compounded the visitors' misery at the close of play.
England took to the crease for the morning session on 456-3 with Cook already on 182, while partner Eoin Morgan began play on 44.
Morgan reached 104 before being caught at mid-off by Sehwag from the bowling of Suresh Raina, ending a 222-run partnership with Cook.
Tim Bresnan helped himself to a knock of 53 from 75 balls before Cook, approaching his triple-century, was caught in the deep by Raina, prompting captain Andrew Strauss to declare on 710.
The tourists' second innings got off to the worst possible start as Sehwag was caught by Strauss off of the bowling of Jimmy Anderson. India resume tomorrow on 35-1.