Kohli's expertise in shepherding the lower order included a maddening final-wicket stand of 57 with Umesh Yadav - the No 11 contributed one run - and allowed the India captain to bring up three figures; the landmark was celebrated by kissing his wedding ring and pointing up to his wife, the Bollywood actress Anushka Sharma, in the pavilion.
Young Curran (3/23) came in as first change to remove openers Murali Vijay (20), Shikhar Dhawan (26) along with no. 3 K.L. Rahul (4) in a space of eight deliveries as India went from a solid start of 50 for no loss to 59 for 3.
The India captain was running out of partners, however, as his team chased down England's first-innings total of 287.
Only Cook fell in the first session, his front-foot defence defeated by a ideal off-break from Ashwin - repaying his introduction in only the seventh over, despite being India's sole spinner here, with telling drift from round the wicket before the ball turned and dislodged the off-bail.
India, 76 for three at lunch, lost their next two wickets on 100.
Stokes then clean bowled wicket-keeper Dinesh Karthik for a duck as the batsman was beaten for both swing and pace.
That was the last delivery of the over and the next ball saw all-rounder Hardik Pandya missed on nought when Alastair Cook dropped a routine chance at first slip off Stokes.
India have always been criticised for their poor close catching but England, with the tourists still on 100 for five, dropped two slip chances of their own, with Malan reprieving Kohli off Anderson.
But Curran returned to have Pandya lbw for 22 with an inswinging yorker.
On his own performance, which included three wickets in eight balls to make the morning England's, Curran said: "Personally it was pretty special".
England, who won the toss, would have been disappointed at being dismissed for under 300 as they marked their 1,000th Test with an all-too familiar batting collapse.
The hosts, playing their 1000th test match, had lost six wickets for 67 runs as they limped to the close on 285 for nine on Wednesday.