After being put in to bat first, Sri Lanka struggled their way to a below par 155/6 at the Pallekele International Cricket Stadium.
West Indies were in cruise control at one stage with the score at 218-2 in the 40th over, but they failed to put on the finishing touches and the home team took the series 3-0.
Cricket West Indies (CWI) have named a 14-member squad for the two-match series, which could see Andre Russell play his first T20I since August 2018.
St Kitts and Nevis Patriots registered their fourth win of CPL 2019.
India are currently leading the three-match ODI series 1-0, after winning the second ODI.
World Cup returnees Fabian Allen, Nicholas Pooran and Oshane Thomas have been handed West Indies central contracts.
After this win, Sri Lanka are now placed at the sixth spot on the points table with eight points from eight matches.
Sri Lanka's top-order fired in unison with Fernando hitting a 103-ball 104, the first century for the Island nation in this World Cup.
Sheldon Cottrell finished with 2-38 as the most successful West Indies bowler.