Flanker Matt Hankin, winger Jack Wilson, number eight Jackson Wray, hooker Jamie George, replacement left wing Nathan Earle and centre Tim Streather scored the Sarries tries in the 51-10 triumph.
Third-choice scrum-half Ben Spencer contributed 17 points, the England Under-20 player landing four conversions and three penalties from seven attempts in an impeccable kicking display, with his replacement Nils Mordt converting the final two tries.
Scarlets replied with a try by flanker Dan Thomas and five points from the boot of fly-half Josh Lewis.
Only a try-saving tackle by right-wing Wilson, covering the opposite flank, stopped the Welsh region taking the lead in the second minute after full-back Kristian Phillips scythed through the home defence.
Former England fly-half Charlie Hodgson put Sarries on the offensive with a perfect penalty into touch a metre from the left corner flag.
They won the resulting lineout before driving Hankin over between the posts for the opening try, leaving Spencer a simple conversion.
Five minutes later, Saracens moved the ball along the line for Wilson to race over in the right corner, with Spencer adding a left-footed touchline conversion.
Scarlets, who had threatened in rapid-fire attacks, opened their account after 21 minutes with a 49-metre penalty from Lewis but Spencer responded with a much easier effort two minutes later.
The Scarlets pack responded with a rolling maul which produced a penalty, kicked to the corner by Lewis, and immediately produced another to force flanker Thomas over for their opening try in the 26th minute. Lewis converted from the touchline.
Spencer kicked his second penalty for Sarries five minutes later, after the Welsh side were penalised at a breakdown in front of their posts.
Wray showed excellent footwork at the back of a Saracens scrum to force the back-pedalling Scarlets to present Spencer with his third penalty.
The next infringement saw Saracens opt for a five-metre scrum rather than a shot at goal and Wray came off the back of the set-piece to power in for their third try, converted by Spencer for a 30-10 interval lead.
The bonus point was secured eight minutes into the second half when half-backs Spencer and Hodgson combined, both displaying fast hands to send George in unchallenged between the posts and leave Spencer another simple kick.
Hodgson, making only his second start of the season after injury, and Spencer made way for Mordt and Neil de Kock, with former England prop Matt Stevens also coming off the bench.
A long pass from Mordt and a short one from full-back Ben Ransom sent Earle in for their fifth try, converted by Mordt who also added the kick when Streather went between the posts for his side's sixth try a minute from time.