India issued a battle cry to Australia Monday as they wrapped up a comprehensive 208-run victory over Bangladesh after a devastating display of spin bowling by Ravichandran Ashwin and Ravindra Jadeja.

Chasing 459 for victory on the final day of their first Test on Indian soil, Bangladesh were bowled out for 250 in an extended afternoon session after stubborn resistance from their lower order.

Ashwin and Jadeja shared eight second innings wickets to help India extend their record unbeaten run to 19 Tests and leave them in prime form for a series against arch rivals Australia later this month.

India skipper Virat Kohli, man of the match for his 204 in the first innings, paid tribute to Bangladesh for their fighting performance but made clear that his thoughts had already turned to Australia.

"Everyone's minds and hearts are on that series and we are keen to start the first Test," said Kohli after seeing off Bangladesh in Hyderabad.

"Everyone is raring to go ... It's a very big series for us."

Australia, currently number two in the Test rankings, land in Mumbai on Monday for a four-Test series against Kohli's top-ranked team.

Kohli, second only to Australian skipper Steve Smith in the batting rankings, will go into the series in red-hot form after hitting his fourth double century since July.

The Indian skipper said he had been making sure that he does "not get ahead of myself" but acknowledged that he was in top form -- albeit in understated fashion.

"It's been coming off (the bat) nicely in the last year," he said.

- Daunting total -

Monday's result had appeared in little doubt after Bangladesh had been set such a massive total in their second innings and the tourists began the final day on 103-3.

Mahmudullah (64) shrugged off poor form to register his 13th Test 50 while young spinner Mehedi Hasan made a gutsy 61-ball 23 to delay the inevitable against the world's number Test side.

But the match ended when Ashwin, who in his 45th Test had become the fastest bowler to claim 250 Test wickets on Sunday, trapped Taskin Ahmed lbw to finish with figures of four for 73.

There was some drama after the umpire originally turned down his appeal but had to change his mind after the decision was reviewed by the Indian team.

Ashwin also dismissed first innings centurion Mushfqur Rahim (23) in the morning session to scupper Bangladesh's only real hope of saving the match, while Jadeja accounted for star batsman Shakib Al Hasan (22).

Mahmudullah then put on fighting partnerships with their captain Rahim and Sabbir Rahman to resist the Indian attack on what still seemed to be a decent batting track.

India had bowled out Bangladesh for 388 in their second innings and decided to build on their 299-run lead after not enforcing the follow-on.

Ninth-ranked Bangladesh were always left playing catch-up after the hosts posted a mammoth 687-6 declared in their first innings.

Rahim said he was "really proud" of his side and hoped that "we can learn from this".

"If we had restricted (them) to 550 or 600 we could have had a chance but it was quite tough out there," he said.

The result meant India maintained their unbeaten record against the minnows and they now have seven wins and two draws in nine encounters.

The Australia series begins on February 23, with the first Test in Pune followed by matches in Bangalore, Ranchi and Dharamsala.