Simpson's surprise podium finish serves as a boost for South African A1 motorsport, with the country set to host the eighth leg of the A1 GP in Durban on Jan 27-29.
France's Nicolas Lapierre took first place in the feature race, moving France 31 points clear of second-placed Switzerland.
Swiss Neel Jani won the sprint race, but was forced out of the feature race with mechanical problems.
France's win was their ninth in 12 starts. They now have 106 points at the halfway mark of the 12-leg inaugural season.
Lapierre completed the 30 laps in 56 min 17.068 sec, ahead of Britain's Robbie Kerr, who finished in 56:20.782, giving the British team their third second-place finish in six feature races.
Portugal were fourth, while China celebrated their first point with fifth place for Tengyi Jiang.
"I was extremely disappointed by the two mistakes I made during the sprint which cost us a podium finish," Lapierre said of his seventh place in the sprint.
"But given the way we had performed in the last two days, we knew we had a chance if I could focus properly. Our pit stop strategy was very good, and the car performed extremely well."
Switzerland started the feature race in pole position but Jani pulled out after 27 laps.
Also starting from pole in the sprint, Jani clocked the fastest lap of 1 min 47.238 sec on the way to victory in the 15-lap race, leading from start to finish.
The seventh leg of the A1 GP will be held Jan 13-15 at Sentul in Indonesia.