The Blues fought back and came close to a number of scores but were frustrated with the final pass going to ground on two occasions. And it got worse before half-time when indiscretion at a ruck resulted in a yellow card for Blues flanker Leon Rogers.
The Blues started the second-half on the back foot and soon found themselves further behind when centre Keiran Jones kicked a penalty to pull the Scarlets further clear.
But a series of second-half introductions saw the Blues' replacements make a massive impact as the home side began to impose themselves on the game. With Blues outside half Calum Hall beginning to get his team playing, the Blues scored a superb try through winger Jarred Evans. Hall added the conversion and the Blues were back in the game.
And the Blues made the most of their momentum and scored a second try courtesy of flying wing Kurtis Williams to secure the win.
A late consolation try from Scarlets' replacement Harry Randall was converted by fellow substitute Joe Chiffi but it was not enough to deny the Blues their first win of the competition.