Hook scored all 19 points for the Ospreys in their win
Scarlets: (6) 6
Pens: S Jones (2)
Ospreys: (9) 19
James Hook went through the card with all 19 points as the Ospreys maintained their Magners League title hopes and all-but ended those of the Scarlets.
Pens: Hook (3)
The west Wales derby failed to inspire the sides, each holding cup hangovers, in a try-less first half at Stradey.
It took a scintillating Shane Williams break from his own 22 to ease Ospreys clear, Hook supporting for the key try.
He added 14 points with kicks, Stephen Jones' two first-half penalties the only scores for the deflated Scarlets.
The Ospreys trail league leaders Leinster by five points, but they have a game in hand over the Irish province who must travel to the Liberty Stadium on Friday.
I didn't think they were the better team, but there were errors all over the pitch
Scarlets director of rugby Phil Davies
Respective losses from the Scarlets and Ospreys to Leicester in the Heieneken Cup semi-final and EDF Energy Cup final seemed to contribute to a poor first half in Llanelli.
In a predictably bad-tempered start following the Ospreys' 50-24 Boxing Day win in the reverse fixture in Swansea, the Scarlets gifted two early penalties to Hook.
The home side gradually got into the game, Regan King going close to a try as Hook fumbled an awkward ball in the slippery conditions on his own 22.
Jones got the Llanelli side on the scoreboard with a penalty, and it took a heavy tackle from Andrew Bishop to deny Gavin Evans a try as the centre went for the line.
Jones' second penalty got his team level, but Hook's third kick restored the visitors' advantage against the run of play.
The west Wales rivals got stuck into a dour battle
On the stroke of half-time, Ospreys number eight Filo Tiatia was sin-binned for another offence at the heavily infringed ruck area, but Jones missed the resultant penalty.
The 14-man visitors held out after the break, while the Scarlets were lucky not to have Dafydd Jones sent to the bin after a stamp at a ruck.
But it took a moment of genius from Williams to break through the gloom at Stradey Park, the Ospreys wing bursting onto turnover ball inside his own 22.
As the try showed, the weather didn't stop us playing our game
Ospreys outside-half James Hook
The Wales star stretched outside three despairing tackles before reaching halfway and breaking to the right.
Williams then found support to the left, Sonny Parker being brought down short as he went for the line, but finding Hook from out of the tackle who crossed for a memorable score.
Brent Cockbain hobbled off with a dead leg that is likely to rule him out of the Leinster game, but Hook completed his run through the card with a 63rd-minute drop goal.
The Scarlets fought back, and after a strong, short-range scrum Ospreys replacement Mike Powell was sin-binned for coming in from the side to kill the ball.
A relentless series of attacks followed, but a determined Ospreys defensive effort denied the home side even a losing bonus point, the Scarlets slipping to their first league loss in Llanelli since September 2005.
Scarlets director of rugby Phil Davies:
"I'm not a happy man, this is supposed to be professional rugby not amateur rugby.
"I didn't think they were the better team, but there were errors all over the pitch - from us, them, the officials, everyone. It was a poor game.
"They finished the try well, but it was pretty average considering this was professional rugby. The players and fans don't take the blame - it was just a poor game."
Ospreys outside-half James Hook:
"The win was the key thing, a loss would have ended our title hopes.
"It was a superb performance, as the try showed the weather didn't stop us playing our game and we deserved the win.
"It's a quick turnaround before Leinster visit on Friday and that's another game we can't afford to lose, so we have to put this result on the back-burner."
Scarlets: B. Davies, M. Jones, King, G. Evans, Watkins, S. Jones, Peel, I. Thomas, Rees, Dunlea, MacLeod, A. Jones, Easterby, G. Thomas, D. Jones.
Replacements: L. Davies for Peel (80), Manu for Dunlea (49), Afeaki for A. Jones (49), Popham for D. Jones (49). Not Used: Owen, C. Thomas, Daniel.
Ospreys: Byrne, Walker, Parker, A. Bishop, S. Williams, Hook, Marshall, D. Jones, B. Williams, Millward, Cockbain, Thomas, R. Jones, Pugh, Tiatia.
Replacements: Terblanche for Walker (80), Spice for Marshall (79), Hibbard for B. Williams (69), Griffiths for Millward (69), Powell for Cockbain (59). Not Used: Beech, Connor.
Referee: Hugh Watkins (WRU)