Rahul was unbeaten on 64 and put on 88 runs with skipper Virat Kohli (45 not out) who was also solid at the crease, as the duo easily crossed Board President XI's 180 all out from day one.
Rahul started the day at 30, while Kohli took first strike as Cheteshwar Pujara (28) had been bowled in the final over on day one, leaving the visitors at 93 for three.
Early on, there was a moment of hesitation from Rahul as he sent back Kohli after he had set off. The throw was off the mark, and afterwards the duo looked in no discomfort on a bright and sunny day.
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The scoring rate dipped a bit, but that didn't matter altogether, except that Kohli quickly caught up with Rahul in the forties. And that is when the discomfort began for the latter. He was a bit edgy in getting his fifty, and thus, there were a couple of further occasions of miscommunication between the two batsmen.
At the other end, Kohli too was almost caught when he tried to flick the ball past the short-midwicket fielder. The Board President XI side was unlucky not to snare one of the two, as on the last ball before lunch, Rahul edged behind off Joseph again only for stand-in keeper Shai Hope to drop the chance.
(REOPENS DEL 48)
Earlier, England paced their innings well with Roy being the early aggressor with a 61-ball 73, inclusive of 12 fours, that was built upon by Root, who stroked his way to 78 in 95 balls.
Captain Eoin Morgan (28) and Jos Buttler (31) got the starts without converting them into a bigger score at the Maharashtra Cricket Association Stadium in Gahunje.
Left-handed Stokes used his bat like a sledgehammer to smack five sixes and two fours on his way to 62 off just 40 balls after reaching 50 in 33 balls.
For India, Hardik Pandya (2/46) and Jasprit Bumrah - who was taken for 79 runs - finished with two wickets each. The most impressive bowler was left-arm spinner Ravindra Jadeja, who not only applied the skids on England early on but also emerged with economic figures of 1 for 50.
Jadeja's Test spin twin Ravichandran Ashwin was unimpressive and gave away 63 runs in eight overs without a wicket to his name.
England began on a brisk note against the Indian medium pace attack with openers Roy and Alex Hales looking comfortable.
Decision Review System (DRS), being used in a 50-over bilateral series in India, was called upon as early as the third over of the game when Roy was given out caught behind off Yadav and got a reprieve through technology.
The in-form aggressive opener thrived on the early escape as he drove the medium pacers when they overpitched.
Just when it seemed that he and Hales would complete yet another half century stand a direct hit from Bumrah in the deep to the non-striker's end caught the latter out of the crease while responding to Roy's call for a couple of runs to arrest the stand at 39 in over No 7.
With the pacemen proving ineffective, skipper Kohli turned to spin and brought on Jadeja who immediately slowed down the run-flow.
After the 13th over Ashwin was brought on from the other end and should have had Roy, on 71, dropped off a top-edged reverse-sweep by Yadav at third man.
Luckily for India the drop did not prove too expensive as Jadeja got the batsman stumped by Dhoni in the next over to snap the second-wicket stand after the addition of 69 runs at 108.
On the umpire giving the batsman not out, Dhoni indicated that the DRS call should be taken and it proved to be a correct call as the decision was overturned and the visitors' skipper sent back for 28.