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Matt Giteau crossed over just short of the half-hour mark for the game's first try, yet once more the visitors hit back through John Barclay, who touched down shortly after.
However, Toulon did have a lead to hold onto at the interval thanks to Maxime Mermoz, who found the try line 10 minutes before the break.
Halfpenny and Priestland were both on hand to kick over once more before the end of the half, in what was a tightly-contested battle between the two sides.
The French outfit pushed on in the second half, however, with Steffon Armitage adding a third try of the afternoon for his side, while Halfpenny found the sticks once more.
The Scarlets did reduce the deficit late on through Kristian Phillips, but Toulon managed to hold out for the opening-game points in Pool Three.