The Sri Lankans made 195 for three before West Indies, poor in all departments, stumbled to 138 for eight from their 20 overs.
Jayawardene, who has already made a century in this tournament, was part of a dominating 166-run second wicket partnership with Kumar Sangakkara.
As he did in his ton against Zimbabwe in the group stage, Jayawardene batted with a cool head and an impressive ability to penetrate the field.
While so many players opt to blast their runs in this format, the former Sri Lankan skipper shows you can prosper with more traditional qualities.
He still produced some big shots in the 56 balls he faced, hitting four sixes and nine fours, but most of the latter were driven or placed through gaps on the ground.
Sri Lanka were helped along their way by some woeful fielding from West Indies who missed out on five catches and a stumping opportunity.
The mishaps in the field were all the more evident coming so quickly after Australia's outstanding catching and ground fielding in their win against India.
A full Kensington Oval, with a partisan home crowd, at the very least expected a decent run chase from their team.
Chris Gayle and Shivnarine Chanderpaul went out clearly aiming to get off to a flyer and they hit 22 from the first 11 balls before Chanderpaul departed.
When Gayle also went, having made just five, Ramnaresh Sarwan and Dwayne Bravo were forced to consolidate and the required run-rate drifted away from them.
