Chasing 145 for victory on a turning track, India slumped to 74-7 in Sunday's morning session, seemingly hurtling towards what would have been their first test defeat by Bangladesh.
However, Iyer and Ravichandran Ashwin (36) then forged an unbroken 71-run stand to frustrate Bangladesh and pull off a thrilling victory for the tourists.
Ashwin was adjudged player of the match for his 42 not out and six-wicket haul, but Rahul singled out Iyer for special praise after his unbeaten 29.
"The way he batted today was phenomenal. He made it look really easy," Rahul told reporters after the nervy three-wicket victory sealed the series 2-0.
Rahul, leading the side in absence of injured skipper Rohit Sharma (35), added, "There was a lot of pressure, there was a little bit of panic in the dressing room, but it didn't look like there was any panic when we were watching Shreyas bat."
Mehidy Hasan (5-63) and Shakib (2-50) wreaked havoc with the ball, but Iyer gave a spin batting masterclass to secure India's victory.
Iyer finished the series with 202 runs from three innings, behind teammate Cheteshwar Pujara's 222 from four.
Ashwin had been given a reprieve on one when Mominul Haque spilled a catch at short leg. That proved a costly mistake in the end, but the hosts had also missed four chances in India's first innings.
"It is slightly disappointing, as other teams don't miss the chances that we are missing," said Bangladesh captain Shakib.
"Those made the difference. We could have bowled them out for 250 instead of 314 (in the first innings). There was a chance in the second innings (too) ... maybe it happens due to lack of concentration or fitness."
