Bangladesh players appeal unsuccessful for Virat Kohli wicket during the third day of the second Test match in Dhaka on Saturday. AP
Axar Patel was unbeaten on 26 for India, which won the first Test by 188 runs, on a tricky, turning surface while nightwatchman Jaydev Unadkat was three not out.
Four of the Indian top five were out for single figures after captain Shakib Al Hasan made the initial breakthrough by dismissing opposite number KL Rahul for two. Mehidy then got in on the act, having Cheteshwar Pujara stumped for six.
Mehidy also had Shubman Gill stumped by Nurul Hasan for seven before removing talisman Virat Kohli for one as he was caught at short leg.
"The wicket is difficult but if one of the batters can play a long innings we can win,” India paceman Mohammed Siraj said.
"Axar looks positive. We hope he will carry on and then we have Shreyas Iyer and Rishabh Pant who are in form."
Bangladesh players celebrate the wicket of India's Cheteshwar Pujara in Dhaka on Saturday. AP
Earlier, Liton Das hit 73 and Zakir Hasan, playing in his second Test, made 51 as Bangladesh was bowled out for 231 in its second innings. Liton was dropped twice by Kohli, who also spilled a chance off Nurul (31).
Liton put on 46 with Nurul and 60 with Taskin Ahmed, who scored 31 not out, after Bangladesh had been reduced to 113-6.
After resuming on 7-0, Bangladesh made a poor start to the day when off-spinner Ravichandran Ashwin trapped opener Najmul Hossain lbw for five.
But Liton and Zakir held the innings together as left-arm spinner Axar worked his way through the batting order with 3-68.
"It’s important to win the game and draw the series,” Liton said. "We know batting in the fourth innings is always tougher on this wicket so we are confident of winning. They still need 100 runs and things won’t be easy. If we can take two wickets early tomorrow it will be our game.”
Bangladesh won the three-match ODI series 2-1.
Rishabh Pant hit a brilliant 100 not out for India on a difficult pitch on Thursday but the deciding Test was still in the balance with South Africa needing 111 to win the match and take the series.
Ashwin was unbeaten on 42 off 62, a knock which included four fours and one six with Iyer on 29 off 46 with four boundaries as India raced to the victory target of 145-7 on the first session on day four.
England, set 378 to win, finished on 378-3 with Joe Root 142 not out and Jonny Bairstow 114 not out.
The South African fast bowler removed opener Mayank Agarwal for 60 and then Cheteshwar Pujara first ball to revive the home team after lunch, and after India made a solid start at SuperSport Park in Centurion.
In a remarkable display of skill and determination, Faisal completed the fastest dive using an underwater wheelchair, clocking an astonishing time of 37 minutes and securing yet another spot in the sporting records.
"Test cricket throws different kinds of challenges, different kinds of pressures," Rohit told reporters. "But the way they have dealt with the pressures throughout the series has been superb."
Babar smashed 111 not out off 63 balls with 14 fours and two sixes and anchored Peshawar to 201-5. Yaqoob left Islamabad shell-shocked after taking four wickets in the penultimate over that included the key wicket of Munro.