It seemed Morgan (49no) had left it too late, with three still needed to win off the final ball from Ashok Dinda.
But the Irishman kept his cool, even after Dinda controversially pulled out of the delivery first time round with Morgan crouched in his stance. An apparent rethink then worked a treat for England as Morgan stood his ground to strike a perfect blow straight back over the seamer's head to tie the two-match series.
It was England's highest ever Twenty20 run-chase, and it saw them conclude their 2012 schedule, with the one-day international series to follow in January of next year.
England had earlier struggled to contain Mahendra Singh Dhoni and Suresh Raina's late onslaught and appeared to be up against it to better 177 for eight at the Wankhede Stadium.
Virat Kohli and Dhoni top-scored with 38, while Raina was unbeaten on 35.
But on a good batting surface, and with a heavy dew making life difficult for India after Morgan had won an important toss, Michael Lumb (50) and then the captain himself scrambled England home.
Even another three economical wickets from Yuvraj Singh could not quite tip the balance India's way this time.
Lumb shared an opening stand of 80 with Alex Hales - and then after Yuvraj had done his worst, Morgan finished the job in company with Jos Buttler.
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- Mahendra Singh Dhoni
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