The ex-England fly-half inspired his side to their first away win in five with seven successful kicks from seven as his team-mates scored four tries in a comfortable victory.
The home humbling means Stade are once again left out of the season-closing title play-offs, the fourth straight year they have missed out.
Wilkinson confirmed after the game that he is on the verge of agreeing to an additional year with Toulon.
"The pressure was on us against a good side but we responded to the challenge perfectly," said Wilkinson.
"We are almost there with regards to extending my stay and I have said all season if I thought I could contribute something to the team next season I wanted to stay.
"I love playing with really good players and good coaches and that is what we have here.”
Second-placed Clermont raised the stakes against Agen, running in 10 tries in a 66-21 drubbing.
Clermont are now unbeaten at the Marcel-Michelin Stadium in 57 contests, and will look to make it 58 next weekend against Montpellier in the European Cup.
Montpellier also prepared for the cup tie with victory, seeing off Mont-de-Marsan 30-17 away from home.
Champions Toulouse ended Racing-Metro's hopes of a 10th straight win with a dramatic 27-26 success, secured by a last-minute try from Vincent Clerc and converted by Lionel Beauxis.
Perpignan were also pipped by the odd point at home, losing 21-20 to Castres at Stade Alme Giral, while Bordeaux-Begles bested Bayonne 39-13.
- Sports & Recreation