Bangladesh were bowled out for 213 and lost the second Test in Dhaka.
Cornwall followed his 5-74 with 4-105 in the second innings, while Jomel Warrican and captain Kraigg Brathwaite picked three wickets each for West Indies.
The day began with West Indies resuming on 41/3, hoping to extend their significant lead and take the game out of Bangladesh’s reach.
However, Taijul Islam led the home spinners and the visitors were bowled out for a paltry 117.
Bangladesh had a seemingly achievable target of 231, especially following the opening stand between Tamim and Soumya Sarkar, who put on 59 runs, with Tamim racing away to a 50.
The part-time spin of Brathwaite broke the stand and removed both openers. When Sarkar fell to Brathwaite, nicking one off the pads to slip, West Indies had the much-needed breakthrough.
It triggered a slide they never really recovered from, with Tamim falling shortly after scoring 50.
Thereafter, the wickets came regularly, despite the batsmen getting starts.
Cornwall was in the thick of things, dismissing Najmul Hossain Shanto in the 22nd over, before running through the tail.
However, for a while, captain Mominul Haque resisted, putting on mini partnerships with Mushfiqur Rahim, Mohammad Mithun and Liton Das.
Haque’s stand with Das frustrated West Indies and added 32 crucial runs to the total, reviving Bangladesh from a slide, and pushed them closer to the target.
It was broken, however, by Warrican in the 42nd over and Cornwall then had Das removed three overs later to put West Indies in the driver’s seat.
The wickets then came quickly, but Mehidy Hasan provided staunch resistance. He farmed the strike, and scored a 56-ball 31 to raise Bangladesh’s hopes and take them to the verge of victory, even smashing two sixes.
However, with the hosts still needing 17 to win, he edged one from Warrican and Cornwall took a blinder at slip to seal a famous win for West Indies. (UNI)