India lost three wickets in the last over, including that of Mahendra Singh Dhoni, to fall short of 150.
Rahul's 47-ball knock contained two sixes and six fours and his partnership of 56 with fellow Karnataka mate Manish Pandey (30 in 26 balls) was the only notable stand.
The hosts lost the series opener in Kanpur by seven wickets and need to win this game to keep the three-match rubber, that ends in Bengaluru on February 1, alive.
Wearing black armbands to mourn the sudden demise of India's under 19 and A team trainer Rajeev Sawant and the father of fast bowler Hammed Shami who is not part of the squad, the home team batsmen failed to get going in earnest.
England surprised captain Virat Kohli and Rahul by using left-arm slow bowler Liam Dawson, who had replaced fast bowler Liam Plunkett in the XI in horses for courses change, to open the bowling with the Tymal Mills.
Kohli struck Mills for a six and a four in successive balls in the next over after surviving the lBW appeal but then was deceived by a slower ball from left-arm Jordan and holed out to long off for 21 off the first ball of the fifth over.
Raina slogged and was caught at long on while Yuvraj missed a sweep and was caught plumb in front of the stumps.
Rahul's innings was the saving grace in this period as he coolly got about getting the runs and also used his feet well against the spinners to cart them around for fours and sixes.
He reached his 50 with a single in 32 balls, inclusive of two sixes and three fours. The innings' 100 came up in the 14th over as the Indian batsmen started attacking Dawson and leggie Adil Rashid even as off spinner Moeen did a good job, taking 1 for 20 in four overs.
Pandey survived on 10 and India's score after 15 overs was 108 for three as the English pacers cleverly mixed it up.
Rahul was finally dismissed in the 18th over when trying to lift Jordan over the mid-wicket region but could not clear the rope and was caught by Ben Stokes to bring Dhoni to the crease with only 16 balls left in the innings.
The former captain could not do much and got out to the last ball of the innings, while trying to heave a wide ball from Jordan and dragging it on to the stumps.
Hardik Pandya and Amit Mishra, included in the XI in place of Parvez Rasool, were both run out for ducks in the same over. Jordan finished with 3 for 22.
Disclaimer: No Business Standard Journalist was involved in creation of this content
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