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In a game marred by handling errors Gareth Bowen and Lee Thomas had exchanged early penalties before the Scarlets were able to take the lead.
A charge down by Scott Quinnell gave the visitors great field position allowing Salesi Finau to break through the defence and feed Barry Davies for the games first try, with Bowen adding the extras.
Thomas pegged the Scarlets back with two further penalties before the interval and with first Quinnell and then Ian Boobyer in the sin bin the Blues were able to build a platform from which Shaun James broke through the defence, allowing Dean Dewdney to finally dive over wide out.
The Scarlets were handed more misery when Finau was stretchered off after being concussed and will now face a battle to overtake the Blues as the season progresses and secure the third Heineken Cup spot for next season.