England Beat India Again
Bairstow, 21, and Ravi Bopara finished what Alastair Cook (50) and Jonathan Trott (63) started as England sentenced India to an eighth defeat of a troubled tour in which they did not manage a single victory over their hosts.
Yorkshireman Bairstow, whose father David played four Tests and 21 one-day internationals for England, shared an unbroken stand of 75 in just 40 balls with Bopara to see his team home with six wickets and almost two overs to spare.
Virat Kohli (107) and Rahul Dravid (69) - the latter in his 344th and final one-day international - had powered India to a total of 304 for six which also owed much to Mahendra Singh Dhoni's late hitting in a 26-ball, unbeaten 50.
But then after England were twice set revised Duckworth-Lewis targets thanks to rain interruptions, Bairstow and Bopara made light of a tight situation.
Opener Craig Kieswetter had contributed initial momentum against the new ball, before going lbw to a Vinay Kumar delivery which appeared to be heading past leg-stump.
Trott, whose first straight six off Kumar was his maiden maximum in a 34-match ODI career to date - had a huge slice of luck on 16 when he drilled Munaf Patel for a catch straight to mid-off only to be reprieved by a no-ball call.
On an increasingly greasy outfield, Munaf slipped and injured his leg - an incident which caused a 10-minute delay before the seamer limped off and out of the remainder of the match.
Trott and Cook's stand of 79 ended when, the very next ball after Dravid dropped a straightforward catch at short fine-leg, Kohli bowled the left-hander with a skilful variation leg-cutter.
As Trott moved past his 50 at better than a run-a-ball, Ian Bell helped to bag three sixes in one Ravindra Jadeja over as England took on the short straight boundary, only to then fail to clear when he tried again off RP Singh.
Dhoni gambled by recalling Jadeja before Bopara had settled, and Trott tried to engineer a boundary into the off-side and chipped a catch to point.
Bairstow was pitched into mission improbable yet marked his debut by slog-sweeping his fifth ball in international cricket for six in a Jadeja over which conceded 15 - and after he and Bopara had plundered 42 in a three-over powerplay, they only had to keep their nerve, which they did admirably.
Bairstow finished with 41 from 21 balls, and Bopara 37 from 22.
Kohli's sixth hundred at this level and his stand of 170 with Dravid had transformed India's innings after an uncertain start.
Ajinkya Rahane ought to have fallen to Steven Finn for only eight but was reprieved by Samit Patel's fallible catching, at third man, after Cook won his fifth successive toss.
The tall seamer nonetheless made sure England's, and especially his frustration did not last when - also at third-man - he made good ground to lunge in and take a fine catch after Rahane somehow managed to flick an attempted swipe to leg off Jade Dernbach in his direction.
Rahane's departure brought Dravid to the crease - and a large contingent of India support duly voiced their loud appreciation for one of their country's finest batsmen.
Patel was unable to keep him company for long, holing out to mid-on in Graeme Swann's first over of off-spin.
But that meant Kohli was in the match, and he and Dravid immediately found a fluency previously lacking.
Their placement and timing helped them find handy boundaries - and with 10 overs remaining, India had the perfect platform for a total in excess of 300.
Dravid's only moment of fortune came when Dernbach was unable to hold a sharp return catch away to his left, on 51, and Kohli needed no luck until he was already past his hundred from only 87 balls.
Dravid fell to the very next delivery, after his 22-year-old partner had gone to three figures, losing his off bail advancing and trying to heave Swann to leg after a 79-ball innings which contained just four fours.
Kohli had nine fours - and a straight six off Patel - when he went shortly afterwards, again just dislodging a bail as his foot slipped in the crease, to go hit wicket off Swann (three for 34).
The double breakthrough gave England some respite. But Dhoni then clubbed five fours and two sixes - the second to bring up the 300.
It seemed England might be up against it to prevail again. But that was reckoning without their ever-increasing resilience, and Bairstow's youthful adventure.
England v/s India 5th ODI Nice Pic
England v/s India 5th ODI Nice Pic