In their final leg of Bangladesh tour, Windies find find themselves levelled at 1-1 in a three-match T20I series and a chance to return home with a silverware.
Rovman Powell hit 50 off 34 balls but succumbed to pressure as West Indies folded in 19.2 overs.
Sheldon Cottrell finished with 2-38 as the most successful West Indies bowler.
Sarkar negated any views of complacency creeping into Bangladesh, who registered a 2-0 clean sweep and won the ODI series 2-1.
The opening pair of Tamim Iqbal and Liton Das and then Soumya Sarkar all fell trying to counter short-pitch deliveries.
Bangladesh and West Indies play two more T20 internationals in Dhaka this week.
West Indies beat Bangladesh by eight wickets in the first T20I at Sylhet on Monday.
Shakib Al Hasan played a lone hand to hit 61 off 43 balls but lacked support.
Rhodes singled out Mehidy, Mustafizur, Kayes, Sarkar and Liton Das beyond Bangladesh's 'big five'.
The win on Friday made this the second best year in ODIs for Bangladesh after 2009.