In the midst of his second spell during West Indies' reply to India's mammoth total of 416, Bumrah unleashed menacing inswingers to dismiss the trio of Darren Bravo, Shamarh Brooks and Roston Chase off successive deliveries.
The 25-year-old's stunning feat allows him to join left-arm paceman Irfan Pathan and off-spinner Harbhajan Singh as the only Indian cricketers to have registered a hat-trick in the conventional five-day format.
The hat-trick ball involved some drama as it required a review from the fielding side to overturn the original not out verdict.
Bravo edged a delivery swinging away from him to KL Rahul at second slip before Brooks was hit flush on the pad and adjudged lbw by the umpire.
The new batsman Chase was then greeted with a sharp full-length ball that struck his toe as Indian skipper Virat Kohli challenged the on-field decision.
Hawkeye technology indicated the ball crashing into a large chunk of the leg-stump, sparking euphoric celebrations among the Indian players with the home side struggling at 13-4.
Bumrah added two more wickets to finish the day with six scalps.
His hat-trick is the 44th such instance in Test history and the first in two years since Moeen Ali achieved it against South Africa.