Sri Lanka, chasing 164 to win, sent India home and sealed a five-wicket victory thanks to Chamara Kapugedera's last-gasp, final-ball six.
Their place in the last four was later confirmed when Australia thrashed hosts West Indies in Tuesday's second match.
Australia will face holders Pakistan in the second semi-final on Friday.
It means the two unbeaten sides of the Super Eights - Australia and England - could yet meet in Sunday's final, though few will write off unpredictable holders Pakistan or talented Sri Lanka in their semi-finals.
The latter, especially on this performance, will certainly provide stern opposition for England.
Last updated: 13-05-2010 from 17:30 until 21:30
12-05-2010 on 10:57
Semi Finals :: ICC World Twenty20 West Indies 2010 :: British West Indies, Carribean
Mathews and Kapugedera picked up the mantle and ensured, with two overs left, they needed 30 to win but just 10 to ensure India's exit.
Few could have predicted the finale, though. Kapugedera smashed two maximums over the long-on boundary and Mathews punched over long-off as Sri Lanka pressed hard - only for the latter to be run out off the penultimate ball with his side still three short of victory.
Kapugedera was the very picture of calm, though, and he carved a glorious six over sweeper cover off the final delivery to see Sri Lanka home and complete India's misery.
source of shift: bbc.com
