The visitors outscored their Welsh rivals by four tries to two, with Ben Thomas claiming the clinching touchdown midway through a second half which saw three yellow cards.
Cardiff openside Dan Thomas put in a mighty display against his former team to take the player of the match award.
Coach Matt Sherratt said: “We talk a lot about fight and resilience and to come back from 15-0 down I thought we showed bucket loads of that.
“I am really pleased for the players that they got what they deserved. To get a derby win away to the Scarlets, after two disappointing results against them last season, you’ve got to enjoy that.”
Scarlets coach Dwayne Peel said: “We started brightly and were in good shape, but we just let Cardiff back into the game.
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