Dilshan was unbeaten on 58 and Silva was not out on 37, as Sri Lanka, sent in to bat, reached 217 for five in their first innings when bad light stopped play 20.
3 overs early on the opening day at Queen's Park Oval.
In between three breaks for rain, Sri Lanka were struggling on 117 for five, but Silva joined Dilshan, and they punished wayward West Indies bowling to put their side back on track.
Dilshan reached his 50 just prior to the close, when he guided Sri Lanka's wrecker-in-chief Fidel Edwards through backward point for two. Silva was no less enterprising with the cut and the pull some of his most productive strokes.
He was dropped on 34 just before the close, when Devon Smith, moving to his right at second slip, failed to hold a sharp chance off Daren Powell.
Greeted by a helpful pitch, things had started well for Sri Lanka who has been put into bat.
Michael Vandort was fortunate that umpire Billy Bowden ruled in his favour, when Powell appealed for an lbw verdict off the s