Earlier, Nathan Lyon kept Australia in the contest, claiming six for 82 to help bowl out Bangladesh for 221 after the hosts had resumed on 45 for one.
Australia bowled out Bangladesh for 260 and then suffered a spectacular top-order collapse of their own to leave them reeling at 18 for three after the spin-dominated opening day of the first Test on Sunday.
Up against fancied India, Bangladesh's ODI captain Mashrafe Bin Mortaza says the home team should be 'realistic' and enter the one-off Test with an aim to achieve a draw.
Demoralised Bangladesh will look to end their campaign on a high when they face a rampaging New Zealand.
Images from the IPL match between Chennai Super Kings and Kolkata Knight Riders, in Mumbai, on Wednesday.
Bangladesh defeated Pakistan by five wickets to qualify for the final of the Asia Cup.
India spinner Ravichandran Ashwin slipped a place to take the third position in the latest ICC Player Rankings for Test bowlers in Dubai on Thursday.
India have a fielded a lot of youngsters for the T20 series against Bangladesh keeping in mind the World T20 in Australia.
The teams are ready to battle it out and with no established name figuring in India's bowling department
Bangladesh's first World Cup centurion Mahmudullah is hoping to extend his big scoring spree at the World Cup when he faces off against India.
India's bowlers faced dogged resistance from Bangladesh middle-order led by captain Mushfiqur Rahim, who hit a defiant 81 not out to take his team to 322 for six at stumps on Day 3 of the one-off Test in Hyderabad.
The visitors were 66 for three in their second innings at the end of the fourth day's play, with an overall lead of 122 runs.
Robin Uthappa and Sunil Narine played lead roles as Kolkata Knight Riders booked a berth in the play-offs of the Indian Premier League after beating Royal Challengers Bangalore by 30 runs at the Eden Gardens in Kolkata on Thursday.
Kolkata Knight Riders took a giant stride towards ensuring a play-off berth as they walloped Chennai Super Kings by eight wickets to take their winning streak to five matches in the seventh edition of IPL.
Bangladesh outplayed Pakistan by 79 runs in the first one-day international in Dhaka on Friday, in only their second win over their rivals in 48 games across all three formats.
Afghanistan will take on Bangladesh in a three-match T20 series, starting Dehradun on Sunday, dividing their focus ahead of the historic Test debut against India in two weeks' time.
India's Kedar Jadhav had six career wickets in one day internationals before Thursday's Champions Trophy semi-final against Bangladesh but it was his very occasional off-spin proved to be decisive in his team's win.
'It's a tournament of the top eight teams and more challenging than the World Cup'
New Zealand and Bangladesh enter their final group match of the ICC Champions Trophy, in Cardiff, on Friday, with the knowledge that even a win may not be enough to see either of them into the semi-finals.
Afghanistan's Rashid Khan came up with a brilliant all-round effort as Sunrisers Hyderabad scored a 13-run victory over Kolkata Knight Riders in the second qualifier and made the final of the Indian Premier League at the Eden Gardens on Friday.
Rohit is currently the highest run-getter in the ongoing World Cup with 544 runs from seven innings that includes four centuries and one fifty.
The number one ODI status will be on the line when second-placed India and table-toppers South Africa clash in a six-match series, starting in Durban on Thursday.
Bangladesh spinners, led by Shakib Al Hasan, guided their side to a thumping nine-wicket win against Afghanistan in their Qualifying Group A match of the ICC World T20 at the Shere Bangla National Stadium on Sunday. Later, Debutants Nepal produced a dominating all-round performance to crush Hong Kong by 80 runs in another qualifying Group A match.
Kumar Sangakkara continued his awesome batting form in Bangladesh as Sri Lanka won the second One-Day International by 61 runs in Dhaka on Thursday to take an unassailable 2-0 lead in the three-match series.
Gujarat Lions were pleasantly surprised to see a seaming track on offer at the Edens Gardens and made full use of the conditions to set up a five-wicket win over Kolkata Knight Riders.
India captain Virat Kohli remained in second spot behind Steve Smith while Alastair Cook jumped nine places to be eighth in the latest ICC Test rankings after his unbeaten double century in the ongoing Ashes.
Tamim Iqbal and Imrul Kayes set a new record opening partnership for Bangladesh when the left-handed duo added 224 for the first wicket in the third Test against Zimbabwe at Chittagong on Wednesday.
India's Test captain Virat Kohli has dropped out of ICC's top-10 list for batsmen in the five-day format.
While their limited-overs side have already savoured victories over the world's top sides, Bangladesh cricket hopes their narrow defeat to England over five days in Chittagong will be a watershed moment for the Test team. Bangladesh sent England crashing out of the 50-over World Cup and entered the quarter-finals for the first time last year, and scored one-day international victories over India, Pakistan and South Africa during a run of six series wins at home.
It is the first time that India have made a clean sweep in a Test series in the West Indies.
Sunrisers Hyderabad mentor VVS Laxman, on Monday, said the franchise would wait for Cricket Australia's decision David Warner
Rajneesh Gupta presents the interesting numbers from the match:
The rain-hit opening Test between Bangladesh and South Africa in Chittagong petered out to a tame draw after the fifth and final day's play was called off without a ball being bowled on Saturday.
The country's Sports Ministry worked closely with the International Cricket Council's (ICC) ACU during the process of drafting the bill.
Mumbai Indians need to rethink their strategy; Narine boost for Kolkata Knight Riders.
India would be aiming to ensure that a plucky Bangladesh don't run away with the momentum when the two sides clash in the second T20 International, which is facing a cyclonic threat, in Rajkot, on Thursday.
Faf du Plessis led from the front as South Africa flexed their bowling muscles to thrash Bangladesh by 52 runs in the first Twenty20 Internationals on Sunday to go 1-0 up in the two-match series.
Mahmudullah Riyadh produced an all-round effort to guideBangladesh to a comprehensive 51-run win against United Arab Emirates, as the host opened their account in the Asia Cup T20 tournament in Mirpur on Friday. Batting first, Bangladesh managed only 133 for eight largely due to rearguard action from Man-of-the-Match Mahmudullah, who scored a quickfire 36 off 27 balls with the help of a boundary and two sixes. However UAE's batting faltered once again as they produced a below-par effort to get bowled out for 82 in only 17.4 overs. Mahmudullah took 2/5 along with a brilliant catch to make it a memorable outing for him. Skipper Mashrafe Mortaza (2/12), left-arm seamer Mustafizur Rahaman (2/13 in 4 overs), Shakib Al Hasan (2/20) and Al-Amin Hossain (1/8) were also amongst wickets. It was a day where Mahmudullah showed his all-round skills taking a smart diving catch at gully to dismiss Shaiman Anwar off Mortaza's bowling.
Former India captain Sunil Gavaskar heaped praise on veteran seamer Ashish Nehra, saying he's a crafty bowler who has proved that "age is just a number".
India will look for another colossal victory and inch closer to the semi-finals when they square off against an embattled Bangladesh.