A chase of 199 was always going to be a daunting one for India and Shikhar Dhawan's third cheap dismissal of the series did not help their case. India lost two early wickets in the chase but a stand between Rohit and captain Virat Kohli steadied the ship for the side.
The loss of both openers in the space of 10 balls did little to slow England and the hosts were 118-2 after 11 overs and a score well in excess of 200 seemed eminently possible.
However, Pandya took 20 runs from the 18th over - bowled by Ball - to put India ahead of the run-rate and turn the match firmly in their favour.
A long tour of England can bring contingencies, and India responded gloriously to the first of those to maintain their clean sheet in T20I bilateral series of three matches.
The sides start a three-game one-day worldwide series on Thursday before playing five Tests.
India made two changes and brought pacers Deepak Chahar and Siddarth Kaul in the XI for Bhuvneshwar Kumar and Kuldeep Yadav. He wasn't bowling as short as he had done earlier but still didn't give England the length to drive or to slog. They got the team off to a flying start. Though the England camp keeps insisting that Ben Stokes, having recovered from a hamstring injury, may not find a place in the XI, he will nearly certainly replace Ball.
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MS Dhoni took the fifth catch of the match, the first wicket-keeper to achieve the feat. His final three overs went for just 16 runs as he finished with figures of 4-38 from his four overs. Pandya had a formality to do and he did well with a six to take India to victory, that too, in style.
The breakthrough came just as India were starting to wonder where to bowl to the opening duo.
IPL franchises were anxious about his lack of T20 match time and he was less attractive because, owing to England's Test series with Pakistan, he would not have been available for the whole season. At one stage, we thought they'd end up getting 225-230. "There was a lot more clarity in the shots that we played".
In the course of his sublime innings, Rohit went past the 2,000-run mark in T20Is, becoming only the second Indian after Virat Kohli to do so.
"It was a brutal day for the bowlers".
Unfortunately for England, the Indian batsmen also enjoyed the bright sunshine and short boundaries in Bristol.
The all-rounder was hit for 22 runs in his first over by Roy but he showed good composure to bounce back in his next three.