Four penalties apiece from Toulon's Leigh Halfpenny and Ian Madigan in an intense encounter at Marseille's Velodrome stadium meant the two teams had to play two extra periods of 10 minutes.
A penalty shoot-out will follow should extra-time finish in a draw.
The winner will play Clermont, 13-9 winners over Saracens on Saturday, in the May 2 final in Twickenham.