Bradley Davies, Tom Jenkins, Tom Isaacs and James Cullen weighed in with tries for the Blues, with Jamie Roberts and Kristian Baller (2) adding the extras.
However, the Scarlets were too strong in the end with
Rhys Priestland crossing for a try and kicking five points with the boot, whilst wing Alec Jenkins, Martin Thomas, Iwan Taffetsausser and no.8 Lee Williams scored the visitors' tries as they edged the verdict.
The Ospreys under 20s bagged their first win of the championship with a 22-13 victory over the Dragons at Maesteg.
Wing James Pike, hooker Mark Breeze and number eight Andrew Gwyn bagged tries in the first half as the home region went into the interval 17-13 to the good - wing Marcus Johnstone and scrum half Robert Lewis crossing for the Dragons.
Ashley Smith kicked a penalty to keep the Dragons in touch, but a try from replacement flanker Ross Cridland midway through the second half gave the Ospreys their first points of the campaign.
Gwyn was outstanding for the Ospreys, who used their driving line out to good effect, whilst home centre Jonathan Spratt and Lewis, for the Dragons, were the pick behind.