Bumrah forced Cook into the drive by pitching it up as the England opener copped another failure.
Moeen Ali was promoted to No.3 but the experiment failed as both Cook and Ali fell in the span of three overs.
Joe Root anchored the English innings and added valuable runs with first Jennings, then Stokes.
Jennings fell on the brink of Lunch, leaving England on 92/3 at the break.
Jonny Bairstow fell first ball after Lunch with England losing two in two balls, leaving Shami on a hat-trick - one which he didn't get eventually.
Root was run-out on 48 off a direct hit from Shami.
Stokes must have played a part in Root's run-out but his stand with Buttler kept England in the game.
Sam Curran once again took on the Indian attack and stretched England's lead ro 233 at stumps after Buttler fell for 69. England ended the day on 260/8.