England were bowled out for 486, a lead of 338, and India crumbled to nine for two before rain forced the players off the field 10 minutes before the scheduled interval.
Vijay was trapped lbw by James Anderson for two and Gambhir, looking for a non-existent single, was run out by a direct hit from Chris Woakes after being sent back by Cheteshwar Pujara.
England, 2-1 up in the series, tore into the Indian attack after resuming on 385 for seven.
Root clipped Ishant Sharma for three through mid-wicket to reach his fifth Test century, celebrating with a leap in the air and flamboyant fist pump.
Chris Jordan, on 20, edged a fierce Sharma delivery through to wicketkeeper MS Dhoni to end an eight-wicket partnership of 82 from 76 balls.
Stuart Broad threw his bat at everything and raced to 37 off 21 deliveries, including a six and five fours, before he gloved a short ball from Sharma to Virat Kohli at third slip.
Root, reprieved on 110 when he was bowled by a Sharma no-ball, continued to plunder the wayward attack and struck a succession of boundaries all round the wicket.
Anderson was lbw to Ravichandran Ashwin for one to end the carnage and Root was left unbeaten on 149 from 165 balls, including a six and 18 fours.
Image: Joe Root celebrates after completing his century
Photograph: Gareth Copley/Getty Images
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