The French outfit began the defence of their continental title in the new-look competition with a battling display on Sunday, as they look to become the first side to win three successive crowns.
They were forced to dig deep in their Pool Three clash at Stade Mayol, but were ultimately helped by Scarlets' indiscipline.
After Scarlets' number eight Rory Pitman had been yellow-carded for a high tackle on David Smith after five minutes, Matt Giteau's sparkling try gave Toulon an 8-3 lead midway through the first half.
But John Barclay responded in kind as Scarlets moved ahead, only for Maxime Mermoz to charge down Scott Williams' kick and score from the restart as Toulon earned a lead they would never relinquish.
The hosts led 18-13 at the break and, after Scarlets hooker Emyr Phillips had been sin-binned, they pulled further ahead through a penalty from Leigh Halfpenny - making his first European appearance for his new club - and a try from Steffon Armitage, who had been the subject of much speculation about a possible return to England in the build-up.
Scarlets, who were mourning the death of former chief executive Stuart Gallacher, did find a late try through Kristian Phillips, but it was too late to salvage a losing bonus point.
Before Toulon's back-to-back wins in 2013 and 2014, Leinster had clinched successive Heineken Cup crowns in 2011 and 2012, and they began this year's challenge with a narrow 25-20 home victory over London Wasps in Pool Two.
Trailing 20-11 at half-time, after scores from Alapati Leiua and Christian Wade had sandwiched a try from Leinster's Darragh Fanning, the Pro12 outfit mounted a second-half comeback.
Fanning crossed for his second of the match, before Dominic Ryan was adjudged to have just touched the ball down on the whitewash as Leinster ran in 14 unanswered points in the second period to seal victory.
In Pool Five, Ospreys ran in five tries as they hammered Treviso 42-7 at the Liberty Stadium.
Dan Evans went over twice, while Jeffrey Hassler, Rhys Webb and Dan Baker also crossed as Ospreys picked up a maximum five-point haul.
Elsewhere, Yohan Huget claimed a brace of tries as Toulouse overcame Montpellier 30-23, with the visitors grateful to Benoit Paillaugue's last-minute penalty for securing them a losing bonus point.
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