Jaiswal and captain Rohit Sharma had edged to 9-0 in the seventh over when Rohit was bowled by Tim Southee as he advanced to attempt a wild drive.
Kohli did not score in his nine balls before gloving 23-year-old O’Rourke, playing his fifth Test, to leg slip.
Sarfaraz was caught at mid-off attempting a counter-attack and, after a short rain delay and a 10-over partnership returning just 21 runs with Pant, Jaiswal cut O’Rourke to point.
Rahul was caught down the leg side in O’Rourke’s next over and an over later, Jadeja skied a catch off a leading edge and Ashwin edged to gully in consecutive balls off Henry.
Henry’s next over returned the wicket of Pant, who poked an edge to second slip, and the seamer produced a fine sprawling catch soon after to catch Jasprit Bumrah’s top-edge at fine leg.
Henry then claimed his fourth Test five-wicket haul by having Kuldeep Yadav caught in the gully.
India’s total was the 18th-lowest by any team in Tests.
