Wales star Hook scored all of the Ospreys' points, including the only try of the game in the second half that settled this full-blooded West Wales derby.
As well as earning bragging rights, victory sent the Ospreys up to third in the Magners League, with a game in hand over leaders Leinster, while defeat all but ends the Scarlets' title aspirations.
The result also denied the Scarlets a League record for back-to-back home wins, ending after a run that began last September and that it was ended by their local rivals will make the frustration of not surpassing Munster's mark all the harder.
Both sides arrived at Stradey Park nursing Cup hangovers inflicted by Leicester Tigers: the Ospreys losing the EDF Energy Cup last time out while the Scarlets crashed out of the Heineken Cup on Saturday.
It was the Ospreys who gained the edge despite the incessant drizzle, leading 9-6 at the break before Hook went over on the hour following a scorching break by Shane Williams.
Ryan Jones stole possession in midfield, Williams did the damage beating four defenders before Sonny Parker turned provider for Hook, who added the conversion and a late drop goal.
The Scarlets rallied late on but the Ospreys defence held firm to put themselves on the shoulder of the league leaders as the title race enters the final straight.
Ospreys: Try: J Hook. Con: J Hook. Pens: J Hook (3). Drop Goal: J Hook
Scarlets: Pens: S Jones (2)