Saracens too strong for Scarlets
Mako Vunipola got the champions on track before Nick Tompkins, an 11th hour replacement for Brad Barritt, Marcelo Bosch, Chris Wyles secured the bonus point.
Rhys Patchell kicked 16 points for Scarlets who briefly hinted at a comeback after Ben Spencer's yellow card with second half tries by Aaron Shingler and Jonathan Davies.
But Michael Rhodes completed a dominant display from the Saracens pack to take charge of Pool 3.
Patchell drew first blood at Allianz Park with an early penalty but Mako Vunipola rumbled over for the opening try in the tenth minute.
Schalk Burger was involved several times as Saracens' forwards drove forward, Alex Goode and Michael Rhodes put width on the attack where Vunipola charged a way through.
Scarlets, who lost Wales centre Scott Williams in the morning of the game with an ankle problem, then saw full-back Liam Williams limp off after just 14 minutes.
Saracens had also lost a centre before kick-off when Brad Barritt pulled out after the warm-up so Nick Tompkins stepped up and scorched over for a try just 26 minutes into his European debut. The centre beat four defenders as he weaved his way between the posts.
Farrell converted and added a drop goal but penalties allowed Patchell to limit the damage to 20-12 at half-time.
Both Vunipola brothers punched holes in the Welsh team's defence, before England fly-half Owen Farrell flung a loopy pass for Bosch to finish on the left wing.
Wyles put the bonus point within touching distance, finishing from 30 metres with aplomb after a Scarlets' handling error.
Shingler scored the visitors' first try of the night just past the hour mark as both sides pursued the extra points.
Replacement eight Josh Macleod thundered off the base of the scrum to set up a second try for Scarlets, with Wales centre Davies powering over from close range.
But South African flanker Michael Rhodes swiftly struck back to secure the bonus point and extinguish any hopes the two tries had fanned of a Scarlets come back.
Tries: M Vunipola, Tompkins, Bosch, Wyles, Rhodes
Cons: Farrell 5
Pens: Farrell 3
Tries: Shingler, J Davies
Cons: Patchell 2
Pens: Patchell 4
Saracens: 15 Alex Goode, 14 Sean Maitland, 13 Marcelo Bosch, 12 Brad Barritt (c), 11 Chris Wyles, 10 Owen Farrell, 9 Richard Wigglesworth, 8 Billy Vunipola, 7 Schalk Burger, 6 Michael Rhodes, 5 Jim Hamilton, 4 Maro Itoje, 3 Juan Figallo, 2 Schalk Brits, 1 Mako Vunipola
Replacements: 16 Jamie George, 17 Richard Barrington, 18 Petrus Du Plessis, 19 Kelly Brown, 20 Jackson Wray, 21 Ben Spencer, 22 Alex Lozowski, 23 Mike Ellery
Scarlets: 15 Liam Williams, 14 DTH van der Merwe, 13 Jonathan Davies, 12 Hadleigh Parkes, 11 Steff Evans, 10 Rhys Patchell, 9 Gareth Davies, 8 John Barclay, 7 Will Boyde, 6 Aaron Shingler, 5 David Bulbring, 4 Jake Ball, 3 Samson Lee, 2 Ken Owens (captain), 1 Wyn Jones
Replacements: 16 Ryan Elias, 17 Luke Garrett, 18 Werner Kruger, 19 Lewis Rawlins, 20 Josh Macleod, 21 Jonathan Evans, 22 Dan Jones, 23 Steffan Hughes
Referee: Pascal Gauzère (France)
Assistant Referees: Maxime Chalon (France), Jean-Luc Rebollal (France)
TMO: Philippe Bonhoure (France)