The in-form Kusal Perera
Earlier, Samuels smashed an unbeaten 110 to guide the West Indies to a competitive 206-9.
Samuels, 34, anchored the innings with his 95-ball knock, hitting one six and 15 fours in the day-night game.
The visitors, who lost the first two ODIs, were off to a disastrous start after being put in to bat at the Pallekele stadium.
Paceman Lasith Malinga (2-43) tasted success in the first over, having opener Johnson Charles caught off the fourth ball by Tillakaratne Dilshan.
Andre Fletcher (six) was trapped leg before off Suranga Lakmal while Dilshan took another catch off Malinga to send back Jermaine Blackwood.
Denesh Ramdin lobbed a short ball from Dushmantha Chameera to wicketkeeper Perera who lunged forward to complete a neat catch and leave West Indies reeling at 18-4.
Samuels then rebuilt the innings almost single-handedly, reaching his second successive half-century and ninth ODI ton in the process.
Sri Lanka had swept the preceding Test series 2-0.