India were in deep trouble midway into the morning session as Virat Kohli (8), Ajinkya Rahane (24) and skipper Mahendra Singh Dhoni (11) were dismissed in quick succession with the visiting side 145 runs ahead and just four second innings wicket in hand.
But, Binny made a mark in his maiden Test with a memorable performance as he not only pulled India out of the woods but also took his side to a lead of more than 300 runs to shut the door on England at Trent Bridge.
Binny also found an able ally in Ravindra Jadela (31) as they put on a crucial 65-run stand for the seventh wicket to keep England - who had scored 496 all out in their first innings - at bay.
India, however, continued to bat and declared their second innings at 391 for nine. The two sides then decided to end the match. Bhuvneshwar Kumar, who shared 91 runs with Binny for the eighth wicket, remained not out at 63, his second half century of the match after his first innings 58.
Binny's solid 78 off 114 balls was studded with eight fours and a six and he was out just before tea break after taking the match out of England's reach. Binny, who showed fantastic temperament in his debut match, looked on course for a century before Moeen Ali had him LBW with 10 minutes to go for tea.
India were 347 for eight at tea break, an overall lead of 308, and by then it was clear that the match would end in a draw. The two sides now move to Lord's in London for the second of the five-match Test series, which begins on July 17.