Fly-half Jones - who ended on five penalties and four conversions - was instrumental throughout and his four first-half penalties helped Scarlets to a 26-15 advantage at the break.
Regan King and Jones both crossed early in the first half to give the Walsh side a commanding lead.
But Perpignan hit back and second-half tires from Adrien Plante, Ovidiu Tonita and Damien Chouly set up a nervy finish to the match.
Leinster also enjoyed a bonus-point victory over French opposition with a 38-22 win over Racing-Metro 92.
First-half tries from Sean O'Brien and Rob Kearney helped them to a commanding 21-6 lead at the interval.
Richard Strauss grabbed his side's third try on 48 minutes but Albert Vulivuli hit back with a superb individual effort.
But Jamie Heaslip and Fergus McFadden added late efforts to secure victory.
Disappointing Cardiff Blues had Casey Laulala to thank as they scraped to a 18-17 win over Edinburgh.
The centre laid on the first try for Chris Czekaj before grabbing a second himself.
Allan Jacobsen had helped Edinburgh to a 10-0 lead before the Blues' fightback however Ben Cairns ensured the scoreline stayed close.
And it was disappointment for Ospreys as a Paul Sackey try saw them slip to a 19-14 defeat in Toulon after Shane Williams had given them the lead.