The visitors completed a tricky chase of 265 -- their highest-ever -- in the last over.
Two no-balls by the experienced Jhulan Goswami did not help India's cause in the last over.
The Indian team is currently playing a five-Test series against England with the last match slated to start September 10.
Binny holds the Indian record for the best bowling figures in ODI format.
The 26-year-old Kerala star gives a glimpse of his range of strokes in the video shared on his Facebook page.
The 37-year-old's 3,619 runs is the third highest from his country and he is Ireland's leading wicket-taker with 114 scalps in ODIs.
Rahim, a former skipper, asked spinner Mehidy Hasan to obstruct Sri Lanka No. 3 batsman Pathum Nissanka during running between the wickets in the second ODI.
Bangladesh defeated Sri Lanka by 103 runs via D/L method in the second ODI to take an unassailable 2-0 lead in the three-match series.
The Rawalpindi Express had threatened Uthappa during the 2007 One-Day International series.
Srikkanth’s game was founded on excellent hand-eye coordination, complete lack of fear, unbridled aggression, along with strokes round the wicket.