West Indies had reached 80 for four from 13.5 overs in pursuit of a victory target of 161 when the players were forced from the pitch by a hail storm and play was called off with Sri Lanka well ahead on D/L.
Sri Lanka thus avenged their defeat by West Indies in the 2012 final.
West Indies needed another 81 runs with 37 balls remaining when the heavens opened and, while they were underdogs at that stage, big-hitting captain Darren Sammy had just arrived at the crease to join the Marlon Samuels (18 not out off 29 balls).
Earlier, Lahiru Thirimanne and Angelo Mathews had helped Sri Lanka post a decent total of 160 for six with rapid 40s lower down the order. The two-time losing finalists had been given a flying start by Kusal Perera, who struck two 6s and two 4s in making 26 from 12 balls, but then West Indies came roaring back.
Perera was bowled by Krishmar Santokie, Mahela Jayawardene was smartly run out without facing a ball and then Kumar Sangakkara was caught and bowled by Samuel Badree as Sri Lanka slumped from 40 without loss to 49 for three.
Sri Lanka were forced to rebuild and, despite Tillakaratne Dilshan's run-a-ball 39 at the top of the order, looked as if they would have to settle for a moderate score. But Thirimanne, firstly, and then Mathews added some impetus to push Sri Lanka beyond 150. Both struck three 4s and two 6s, with Thirimanne scoring 44 from 35 balls before falling with the total on 121 while Mathews made 40 from 23, most of them in an onslaught that produced 32 runs from the final two overs to give Sri Lanka the momentum.
n History will not be on India's mind when they face South Africa today in the other semi-final.
India are not only favourites to defeat the Proteas, but also win the tournament and become the first team ever to hold all three major global limited overs titles. They are the reigning World Cup winners, while they won a tight Champions Trophy final against England in Birmingham last June.
The notion of completing an unprecedented treble is, however, the furthest thing from their minds. "We've never believed in talking about these things, because it's only going to make things tougher," said off-spinner Ravichandran Ashwin.
"The one thing that gives this young side an advantage over the other teams is that we don't have any baggage. We've not lost many big competitions, there will be no scars with us. We have nothing to lose."
By contrast, South Africa have a miserable record in major tournaments, earning themselves an unwanted 'chokers' tag.