The 30-year-old medium-pacer sealed India's victory in the second ODI from just 28 deliveries, as Bangladesh were bowled out for 58, chasing India's modest 105 all out.
He dismissed Mushfiqur Rahim for 11, then the hosts' top scorer, Mithun Ali, for 26 before demolishing the middle order and tail-enders.
Mohit Sharma took the other four Bangladesh wickets for 22 runs.
Binny, the son of former India World Cup-winning player Roger, was named man of the match as India took a 2-0 lead in the three-match series.
"At the break we just spoke of bowling in good areas and coming hard at them," said Binny after overhauling Anil Kumble's previous India best of six for 12.
"I'd love to bowl on this wicket every day."
India's 105 all out was their lowest total against Bangladesh, with Taskin Ahmed doing the damage with five wickets for 28 runs.