The former England fly-half scored 27 points in total to add to Steffon Armitage's first-minute try.
But it was a nervy encounter as Stade Francais led for most of the first half and edged ahead once more on the hour, and Wilkinson needed four attempts to settle the match in his side's favour.
Toulon took the lead through Armitage's superb score and they almost had another inside four minutes following more good work by the flanker, only for scrum-half Sebastien Tillous-Borde to drop the ball as he tried to offload from a tackle.
But poor tackling let Morgan Turinui through to set up full-back Hugo Bonneval for a converted score in the 12th minute which nudged Stade ahead.
Fly-half Jules Plisson kicked two penalties and a drop goal to extend the visitors' lead to 16-5 but Wilkinson was on target with penalties in the 32nd and 40th minutes, either side of Plisson's third, to leave the half-time score at 19-11 to Stade.
Wilkinson took his side into the lead with three penalties and a drop goal in the first 15 minutes of the second half but Turinui rounded off a wonderful passing move from the base of a scrum to restore the visitors' advantage, Plisson adding the extras to make it 26-23.
Two Wilkinson penalties countered by a Plisson drop goal left the scores level at 29-29 going into the final 10 minutes - but with Stade winger Julien Arias in the sin-bin for cynically preventing a try after Plisson's kick was charged down.
Wilkinson missed the resulting penalty and then a drop-goal attempt before remarkably putting a 30-metre effort wide from a central position - but he kicked the crucial drop goal from just over 40 metres a minute from time to ensure his side will face Biarritz or Brive in the May 18 final.