Tigers target revised to 151 off 16 overs after rain
But Bangladesh can only reach 145-6 despite Das' stunning 60 oof 27 balls
Kohli hits his third fifty of the competition
India 184-6 (20 overs): Kohli 64* (44), Rahul 50 (32); Mahmud 3-47
India move top of Group 2 and will reach semi-finals if they beat Zimbabwe in final game
Bangladesh need to beat Pakistan and hope others results go their way
That's all from us for today.
My colleague Ffion Wynne's report from a thriller in Adelaide is now live.
In case you missed it, the match report from Netherlands' win over Zimbabwe is here.
We will be back tomorrow morning for coverage of South Africa's match against Pakistan from Sydney. If it is as half as eventful as the India-Bangladesh match then we are in for a treat.
Until then, farewell.
More from India captain Rohit Sharma: "In my opinion [Kohli] was always there, it was just a matter of a few innings which he got in Asia Cup and the form he's shown we know he has got experience playing in big tournaments and we never had any kind of doubts.
"I was quite impressed with how KL Rahul batted as well, we know what kind of player he is and it puts the team in a very different position.
"I thought the fielding was brilliant. Some of the catches we took under pressure were great to watch and when you're playing in front of such a big crowd it's not easy and it shows the character of the team.
"You can have some bad days on the field but luckily that wasn't for us today."
India's captain Rohit Sharma: "I was calm and nervous at the same time but it was important for us as a group to stay calm and execute the plans because it was a shortened game and could go either way with 10 wickets in hand, but I thought we held our nerve pretty well and it was a good win in the end.
"When [Arshdeep] came onto the scene we asked him to do the job for us and someone has to take that role and it is a tough one. He is such as young guy at this point in his international career.
"It's not easy but we prepared him but obviously there was a choice between Shami and him but I had to back someone who was doing it regularly for us."
Bangladesh captain Shakib Al Hasan: "It has been the story of us against India. We are always almost there but never cross the line.
"It was a good game. The crowd enjoyed, we enjoyed it. But in the end someone had to win and someone had to lose."
On Litton Das' form: "He is batting really well. He is probably our best batsman at the moment. The way he batted in the first six overs gave us a lot of momentum and we started to believe."
On bowling Taskin Ahmed out at start of India's innings: " Our plan was to get India's top order out quickly and Taskin has been our main bowler. Unfortunately he couldn't get wickets today but he was unlucky and very economical."
On the rest of their World Cup: "We have been very relaxed this tournament. We have not been talking about it in the dressing room. We wanted to enjoy this World Cup. We played a good game of cricket. We have one game left and I hope we can continue this."
India's batsman Virat Kohli: "It was a pretty close game, not as close as we would have liked it to be but it was another good day with the bat and I was just trying to play myself into the innings.
"Today was another good day with the bat and I was just trying to play myself into the innings.
"Today was different and I felt like I was striking it really well. I'm just in a happy place I don't want to compare and this present moment I'm happy to contribute for my team.
"As soon as I knew the World Cup is in Australia I was grinning. You need good shots here like the ones you play in the Subcontinent.
"I played a lot of good cricketing shots its just an extension for me in any format and I know that kind of game awareness would come in handy.
"I absolutely love playing in this crowd. It makes me feel at home and this ground and wicket has been really kind to me."
Virat Kohli has been named the player of the match after his superb 64 from 44 balls set up the platform for victory.
We will hear from him shortly.
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Henry Moeran
±«Óãtv Test Match Special commentator
It was so close and Bangladesh's hearts are broken.
The India supporters in the crowd roar with delight. There's some Bangladesh fans in tears. They were so, so close to a memorable win.
What a remarkable rollercoaster match that was.
Here comes the final ball from Arshdeep Singh.
Nurul Hasan smacks it.....
....but does not get enough power on it and they can only run one!
India win an absolute thriller!
Henry Moeran
±«Óãtv Test Match Special commentator
And its still not over...
It's full again from Arshdeep Singh but Nurul Hasan has cut it away for four!
Seven needed from the final ball - six for a super over!
That's well run.
It's another full delivery from Arshdeep Singh but Nurul Hasan digs it out and Bangladesh run two.
11 needed from two.
Target 151
Well bowled Arshdeep Singh. He fires in a yorker and Nurul Hasan cannot get it away. Dot ball.
13 from three balls needed.
Henry Moeran
±«Óãtv Test Match Special commentator
It's still not over!
Target 151
Oh my that is huge!
Arshdeep Singh comes around the wicket to Nurul Hasan and he has clubbed it away for six!!
13 from four needed.
Henry Moeran
±«Óãtv Test Match Special commentator
Bangladesh need something special. India are closing in.
Target 151
Swing and a miss from Taskin Ahmed but Bangladesh are able to scramble a bye.
19 needed from five balls.
Another swing and a miss from Nurul Hasan - who appeals for the wide. The umpire says no.
There are few boos from the Bangladesh fans in the crowd, but the replays showed the umpire made the right decision.
20 needed from the final over.
Arshdeep Singh to bowl it.