Wilkinson's haul - consisting of five penalties and a conversion - was supplemented by a second-half try from Steffon Armitage as Toulon ran out 22-14 winners at Cardiff Arms Park.
Cardiff scored the opening try inside two minutes, the ball being moved quickly from a scrum to Tom James on the left wing. James stretched his legs, drew his man and released Leigh Halfpenny on the inside for a run to the line.
Halfpenny failed with the conversion and Toulon stand-off Wilkinson soon showed him how it's done, landing a pair of penalties to move his side 6-5 ahead after quarter-of-an-hour.
Cardiff suffered a further blow when outside centre Gavin Evans was stretchered off after slipping and taking an accidental blow to the face in a collision with Toulon Delon Armitage.
Halfpenny scuffed one penalty chance after a lineout infringement, made amends just before half-time to give Cardiff a 9-8 advantage at the break and then slipped over and missed a third penalty chance in the 51st minute.
A penalty exchange between Wilkinson and Halfpenny, albeit after again not making clean contact, meant the Blues held a one-point lead with less than 20 minutes remaining.
But Toulon struck the decisive blow in the 63rd minute, Matt Giteau setting up a close-range finish for Steffon Armitage after breaking the first line of defence with a show-and-go.
The conversion made it 19-11 to Toulon and Wilkinson answered a further penalty from Halfpenny to close out the result.
Cardiff would have to break new ground to make the quarter-finals as no side has ever qualified after losing their losing their opening two matches.
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