However Gunathilaka's demise to pacer Alzarri Joseph for 36 triggered a gradual decline to 151 for six with left-arm spinner Akeal Hosein taking three for 33 while Jason Mohammed snared his sixth wicket of the series by bowling Karunaratne for 31.
The 27-year-old Jamaican led the initial batting charge for the West Indies, hitting five fours and a six off off-spinner Nayeem Hasan straight over long on.
Resuming on 110-3, the pair put on 216 for the fourth wicket to frustrate Bangladesh's bowlers until they were separated by left-arm spinner Taijul Islam.
The return of wicketkeeper BJ Watling has allowed Tom Blundell to return to his opening slot alongside stand-in captain Latham while Will Young moves to number three.