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Scarlets led by 14 points after a frantic first half with Aaron Shingler, Jonathan Evans and DTH van der Merwe scoring tries.
Hadleigh Parkes' score - following a superb break by Rhys Patchell 30 seconds after the break - clinched the bonus point and the game.
Blues could add only a diving Blaine Scully try to Tom James' early score.
After losing their first three games of the season, Scarlets overtake the Blues - who have lost their last three - to move into sixth place in the Pro12 table.
The absence of 13 first-choice players on Wales international duty did little to detract from the atmosphere and excitement, although some of the defending was less than top-class.
A noisy Friday night crowd were whipped up by four tries in the opening 23 minutes.
And they really found their voice during a series of re-set scrummages lasting more than seven minutes before the interval, which eventually resulted in props Taufa'ao Filise and Wyn Jones being shown yellow cards.
Scarlets held out under intense pressure with the home crowd baying in vain for referee Lloyd Linton to award a penalty try.
Their sense of injustice was further fuelled when Patchell, playing at the Arms Park for the first time since leaving Blues for Scarlets, broke from his own half to set up Parkes from the restart.
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The meeting of the Shingler brothers was another sub-text for the fixture and took its own farcical twist when Aaron was shown a yellow card after being tackled without the ball by Steven.
Blues eventually claimed a try when Scully scored acrobatically, but in spite of dominating possession and benefitting from a lopsided penalty count, they could not close the gap further.
Forwards Ryan Elias, Will Boyd and Shingler were outstanding in a dominant Scarlets display at the breakdown, the visitors aided by a misfiring Blues lineout.
Cardiff Blues: Matthew Morgan; Blaine Scully, Cory Allen, Rey Lee-Lo, Tom James; Steve Shingler, Tomos Williams; Rhys Gill, Kirby Myhill, Taufa'ao Filise, George Earle, James Down, Macauley Cook, Josh Turnbull (capt), Cam Dolan.
Replacements: Matthew Rees, Brad Thyer, Dillon Lewis, Seb Davies, Shane Lewis-Hughes, Lloyd Williams, Jarrod Evans, Dan Fish.
Scarlets: Aled Thomas; DTH van der Merwe, Steff Hughes, Hadleigh Parkes (capt), Steff Evans; Rhys Patchell, Jonathan Evans; Wyn Jones, Ryan Elias, Werner Kruger, Tom Price, David Bulbring, Aaron Shingler, Will Boyde, John Barclay.
Replacements: Emyr Phillips, Dylan Evans, Peter Edwards, Lewis Rawlins, James Davies, Aled Davies, Dan Jones, Ioan Nicholas
Referee: Lloyd Linton (SRU)
Assistants: Cammy Rudkin (SRU), Dai Cambourne (WRU)
TMO: Neil Paterson (SRU)
Scarlets claimed a fourth consecutive Pro12 success with a bonus-point win over Cardiff Blues at the Arms Park.