England needed 24 off last two overs, got 16 of those in the 19th bowled by Ashish Nehra before falling short of the target in the last over from Bumrah in which both Root and Jos Buttler got out to hand India a five-run win.
However, England ended the innings strong after they picked five wickets in the final three overs to restrict India to 144 for eight in the 20 overs.
To succeed as a bowler in limited-overs cricket, especially at the death, it is important to possess the combination of variety and the nerve to deliver under pressure.
England needed just seven runs off the final over in Nagpur to take the win but the series will now be decided in the final match in Bangalore on Wednesday 1 February.
Needing six runs of the last ball, Moeen Ali failed to connect with the Bumrah delivery. Bumrah certainly had that going in his favour and he put it on display to come out with flying colours. The left-hander was bowled for a first-ball duck but survived because Mishra had overstepped.
England were forced to rebuild their innings from 22-2 after openers Jason Roy and Sam Billings fell to veteran left-armer Ashish Nehra, and a patient approach followed as runs were accumulated patiently.
Root and Eoin Morgan (17) began rebuilding as they had done so well in the first game but Amit Mishra snapped up the wicket of the skipper and may have had Ben Stokes in the same over had he not overstepped.
Chris Jordan, with three for 28, and Moeen Ali, whose four overs cost just 20, were the pick of the English attack but India were just as accomplished in the field.
Reeling at 69/3, Rahul was joined at the crease by another youngster - Manish Pandey - and the duo stitched a brilliant partnership to steady the ship for the hosts.
Jordan was in the thick of action early on as he celebrated the big scalp of opposition skipper Virat Kohli. Sensing his threat, Morgan gave him a slip against Yuvraj Singh, who should earlier have been given lbw by Shamshuddin but was eventually dismissed sweeping after a torturous four from 12 balls. He had raced to 21 off 14 when Jordan outwitted him with a slower delivery to have him out caught at long-on.
By the end of the six-over powerplay, India were 46-1, a frenetic mix of hoicks and swipes leavened by some genuinely fine timing from Lokesh Rahul.
Jordan finally got the risky Rahul back in the pavilion in the 18th over to check India's surge as the hosts lost wickets in a heap.
KLRahul scored 71 off 47 balls during India's innings in the second T20Iin Nagpur. Then came the moment that looked to have decided the chase, Buttler producing the most extraordinary flat-bat swipe over mid-on for six.
Though English opponents have the chance to take it on their way in the death overs but then struck Jasprit Bumrah in the last over and hit the last nail in the coffin.