Skosan, a summer signing from the Sigma Lions, enjoyed a dream night at cinch Stadium at Franklin's Gardens, making the most of some slick Saints play.
The South African wing showed off his acrobatic ability with a sensational finish for his second score and eventually became only the fourth player to score a hat-trick on debut in England's top league.
For Worcester, it was a sobering experience as Saints had their try bonus point in the bag inside just 31 minutes.
Tommy Freeman and Alex Mitchell both scored twice, with Dan Biggar, Rory Hutchinson, Api Ratuniyarawa also notching as Saints secured their fourth win in five Gallagher Premiership games this season.
The night had started badly for Worcester before the game even began as scrum-half Willi Heinz and centre Ollie Lawrence were forced to withdraw due to injury.
And things got worse for the Warriors when the game kicked off as wing Duhan van der Merwe was sent to the sin bin for a tip tackle on Sam Matavesi.
Saints soon made the away side pay as Biggar took a quick tap penalty and charged over the line for a score on his 50th appearance for the black, green and gold.
Biggar missed the conversion from a tricky position and Worcester hit Saints with an immediate sucker punch.
Will Chudley charged down Hutchinson's attempted clearance kick and scored, before Fin Smith added the extras to put his side 7-5 up.
But the Warriors lead didn't last long as Saints pieced together a magical move with dummy runs galore, allowing Mitchell to score on his 50th Premiership appearance.
Biggar kicked to make it 12-7 but the Wales star soon found himself on the wrong side of referee Ian Tempest, allowing Smith to strike a penalty that cut the gap to two points.
Worcester welcomed van der Merwe back on to the field with less damage done than may have been expected.
But Saints soon got stuck into the Warriors again as Mitchell made more inroads before sending Ratuniyarawa for his side's third try.
Biggar converted and the hosts had three tries with just 22 minutes gone.
Saints should have had their bonus-point score soon after as Biggar did brilliantly to break the line and offload, but Freeman took too long to pass the ball to Ollie Sleightholme and the chance was gone.
But Worcester were all at sea and Saints were starting to fly, with Skosan soon striking on his debut after chasing down a grubber kick.
Worcester were hit again soon after as Hutchinson intercepted inside his own half and turned on the turbos to score in the corner.
Biggar kicked both conversions to make it 33-10, and that was how it stayed at half-time.
Saints were forced into a change at the break, with Piers Francis coming on to make his first appearance of the season, in place of Sleightholme.
But the one-way traffic continued as Worcester remained submerged, allowing Skosan to score with a stunning acrobatic finish in the corner.
Biggar kicked the conversion from the touchline and Warriors were most likely wishing they could head home, with more than half an hour still to play.
Another eye-catching Saints score was to follow as Fraser Dingwall gathered a high ball just inside his own half, slalomed his way through superbly and offloaded to Freeman for the try.
Hutchinson missed the conversion with Biggar down receiving treatment for an injury that he was just about able to shake off.
Saints turned to their bench to ensure the momentum remained and with an eye to resting players ahead of next weekend's home clash with Leicester Tigers.
But it made no difference as Worcester remained under pressure, with Skosan completing his hat-trick in style after the ball was worked wide to him once more.
Francis was forced off for a head injury assessment, bringing Mitchell back into the game.
And Mitchell was able to score once more as he intercepted inside the Worcester half and sprinted home for his second try of the night.
Biggar converted, and he was doing so again before the end as Saints finished things off with Freeman's second try.
Saints: Freeman; Sleightholme (Francis 40), Dingwall, Hutchinson, Skosan; Biggar, Mitchell (Lomani 57); Waller (Iyogun 56), Matavesi (Haywood 56), Hill (Painter 56); Ribbans (Coles 60), Ratuniyarawa; Lawes (Wood 54), Ludlam (c) (Augustus 57), Harrison.
Worcester Warriors: Shillcock; Doel, O Morris, Venter, van der Merwe; Smith (Heward 65), Chudley (Simpson 54); Sutherland (Waller 72), Annett, Judge (Owlett 60); A Kitchener, G Kitchener (Batley 60); Hatherell, Lewis (Vailanu 56), Kvesic.
Referee: Ian Tempest