At the break, Pandya was unbeaten on 108 (93 balls, 8 fours and 7 sixes) while Umesh Yadav was batting on 3 as they added 66 runs for the last wicket.
With India resuming at 329 for 6, Pandya and Wriddhiman Saha (16) looked to bat for time in a bid to resurrect India's floundering first innings.
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Kuldeep Yadav (26) batted resolutely though and put on 62 runs with Pandya for the 8th wicket.
In doing so they took India past 400 in the 110th over, something that seemed unlikely at stumps on day one. The former then fell immediately afterwards caught behind off Lakshan Sandakan (4-132).
India became the first team to score 400-plus in three successive Tests of a series on Lankan soil.
Pandya then went into overdrive and put on 20 runs with Mohammed Shami (8), whilst reaching his half-century off 61 balls.
He then put Malinda Pushpakumara (3-82) to the sword in the 116th over, taking 26 runs off him with 3 sixes and 2 fours.
It was the most runs scored by an Indian batsman in an over in Test cricket, beating the previous joint-record of 24 runs held by Sandip Patil and Kapil Dev.
The attack helped put an aggressive 10th wicket stand for India as Umesh Yadav and Pandya put on 50 runs off only 26 balls in the extended morning session.
Pandya then reached the three figure mark, his second half-century coming off only 25 balls. It was also his highest First-Class score.
It was also the second fastest Test hundred overseas by an Indian batsman, second to Virender Sehwag's 78-ball effort against West Indies at Gros Islet in 2006.
On day one, Shikhar Dhawan (119) and KL Rahul (85) put on the highest opening stand of 188 runs on Lankan soil before losing their way towards the end.
India lead the three-match series 2-0 after winning the first Test in Galle by 304 runs and the second Test in Colombo by an innings and 54 runs.
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