India swept the two-match series 2-0.
Chasing 145 for victory on a turning track, India reached the target in the first session on the penultimate day, thanks to an unbeaten and fighting 71-run partnership between Ashwin and Iyer from a precarious 74 for 7.
India started the day at 45/4, but lost Jaydev Unadkat (13), Rishabh Pant (9), and Axar Patel (34) in quick succession early in the session.
But Ashwin and Iyer showed great intent and counter-punched Bangladesh’s spin attack with their stubborn batting to take India over the line.
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Ashwin, who remained unbeaten on 42, whipped Mehidy Hasan Miraz towards mid-on for a boundary to take India home, while Iyer made an undefeated 29.
The come-from-behind win meant India wrapped up the series 2-0 to strengthen their chances of a second straight final appearance in the World Test Championship.
For Bangladesh, Mehidy was the pick of the bowlers with a five-wicket haul (5/63)
Bangladesh spinners were all over the Indians after the start of play on Sunday. Resuming the innings at 45 for four, India lost Unadkat (13) in the second over of the day. After slog sweeping Miraz for a six, Unadkat was caught plumb in front of the stumps with a slider from Shakib Al Hasan. Unadkat took the review in desperation but ended up wasting it.
India’s crisis man Pant walked into the middle and tried to put the pressure back on the opposition with his counter attacking approach. The southpaw had changed the course of the first innings with his 93 but fell for nine on this occasion with Miraz trapping him leg before.
It became 74 for seven when a well set Axar Patel (34) became Miraz’s fifth wicket. It was the straighter one again that thud into his pads before clipping the leg stump.
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India were staring at their maiden defeat against Bangladesh before Iyer and Ashwin provided a ray of hope with a gritty stand.
The duo was happy to preserve their wicket initially before Iyer changed the momentum with back-to-back boundaries off Shakib in the 41st over.
Miraz offered a loose ball in the following over and Iyer was quick to make room and punch it through cover for another boundary.
Bangladesh resorted to pace in their bid to break the stand but the plan did not work. Ashwin, who was dropped at short leg on one, collected a couple of boundaries off right arm seamer Khaled Ahmed to bring the target down to just 26 runs.
Miraz was brought into the attack as the last throw of dice but Aswhin pulled him for a six before back-to-back boundaries, sealing the win for the visitors.
Despite the win, India have a lot of thinking to do going into the home series against Australia. The form of the top-order is a big concern.
India dropping Kuldeep Yadav after his five wicket haul in the previous game also became a big talking point of the game.
(With inputs from PTI)