The Llanelli-based side came into this game having lost just once in their last nine matches in all competitions, and had already beaten the Newport Gwent Dragons and Cardiff Blues away from home this season.
But the Ospreys had other ideas and this runaway victory sees them leapfrog over the Scarlets in the league standings.
They had one try from James Hook in the first half, and six more after the break from Jonathan Thomas, Biggar, Richard Fussell, Tommy Bowe, Paul James and Jamie Nutbrown - making it six victories on the trot against the Scarlets.
The visitors had a try apiece from Gareth Maule and Jonny Fa'amatuainu in the second half, and were 20-3 adrift at half-time. Sin-binnings for Martin Roberts and Sean Lamont also dented their hopes of mounting a comeback.
This regional tie had been delayed 24 hours from the scheduled Boxing Day kick-off because of frozen pipes at the Liberty Stadium.
The pitch had been playable thanks to the undersoil heating but health and safety issues regarding the lack of running water in three of the stands meant that the game had to be postponed.
But it was the Scarlets who froze when the match eventually kicked off. Apart from the opening few minutes the Ospreys completely dominated the first half as they assumed a 17-point advantage by the interval.
Dominance at the set piece and at the breakdown as well as Scarlets' indiscipline allowed to the Ospreys to take control of the match.
But the Scarlets were good value for an early 3-0 lead, courtesy of a Rhys Priestland penalty, before the home side turned the screw for the rest of the half.
The Scarlets did not help themselves by conceding soft penalties after 9, 14 and 18 minutes - all kicked by man-of-the-match Biggar.
And the Ospreys went a long way to winning the game with a try from centre Hook in the 25th minute. The move started when a long throw form a Scarlets lineout went astray, with Mike Phillips gathering before Fussell and Bowe combined well to put Hook over in the left corner.
Problems at the scrum saw the Scarlets concede two more penalties after 34 and 39 minutes which the on song Biggar made no mistake in converting for a handsome half-time lead.
The Scarlets' problems increased at the start of the second half when scrum half Roberts was sin-binned for dissent and they conceded two tries in the space of two minutes through Thomas and Biggar, who ran back a loose kick from Priestland.
Against the run of play, centre Maule grabbed a try back for the Scarlets but the Ospreys hit back with another three tries in the space of nine minutes as Fussell crossed to secure the bonus point with Bowe and replacement prop James following suit.
With Ospreys replacement lock Ian Evans earning a yellow card for a stamp, Fa'amatuainu gave the Scarlets' score a bit of relative respectability with a try from a quick tap penalty.
But appropriately it was the home side who had the final say with a try for replacement scrum half Nutbrown.
Biggar, whose side now sit seven points behind table toppers Munster, said afterwards: "It was worth the wait. The boys were superb at times today.
"To come back here in front of a packed house and to put on a show for them was pretty special. It's not bad playing behind a pack of forwards that is going so well at the moment. It makes our jobs as backs pretty easy.
"We're obviously delighted in the dressing room at the moment. There was frustration all round yesterday but we didn't allow ourselves to get rattled by the delay, we've come in today and done our jobs.
"All credit to the fans, I think the general feeling was that the crowd would be way down today because of the problems of people not being able to make it after it was rearranged at short notice, but we had more than 18,000 here in the end and we are just glad that we were able to repay them for their efforts,
"We are building up a bit of momentum after the wins against Munster and the Scarlets, we've had big crowds and we need to keep that going into a huge month in January."
|Ospreys Score Card|
|Scarlets Score Card|