The Scarlets stretched their lead after the break when Williams found a huge hole in the Blues midfield to scamperthrough and send lock Day over for an unconverted try.
Poor shot selection saw three wickets fall in the first 14 deliveries while Naeem, who had launched Darren Sammy over mid-wicket, was needlessly run out trying to scamper a single after the ball had whistled through to the wicketkeeper.