The ART driver was investigated by the stewards after Saturday’s race for forcing Marcus Armstrong off track at Turn 11 in the battle for third place.
They determined that Pourchaire was “unable to hold the line, ran wide and forced Car 7 off track,” adding that “Car 10 was wholly responsible for the incident.”
Pourchaire said after the session that he felt he had kept on track and it was a “fair move” on Armstrong.
The penalty drops the Frenchman to seventh place, with championship leader Felipe Drugovich promoted to third.
Juri Vips and Armstrong were also handed penalties for other incidents during the final laps of the race.
Armstrong was given a five-second penalty for causing a collision with second-place finisher Jehan Daruvala during their battle for second, which preceded Pourchaire and Armstrong’s lap 19 tussle.
The Hitech driver was judged to be wholly at fault for the collision, which saw him make an inside pass attempt at Turn 8, making contact with Daruvala before running wide, while the Prema driver was also forced off track.
Vips was handed a five-second penalty for making contact with Armstrong at Turn 15 on the final lap, where he forced his team-mate off track, dropping him down the order to finish ninth.
Vips’ penalty sees him classified in 11th, falling outside the points, while Armstrong drops five places to 14th.
Logan Sargeant, who is second in the drivers’ standings, is promoted to eighth as a result, the final points-paying position.
All three drivers received a penalty point on their licence for the incidents.
Elsewhere, Enzo Fittipaldi was handed a five-place grid drop for Sunday’s race for causing a collision with Roberto Merhi at Turn 8.
The Charouz driver attempted to pass Merhi, who is driving for Campos Racing in place of an injured Ralph Boschung, up the inside, but ran over the kerb and collided with him.
Fittipaldi was then collected by Van Amersfoort Racing’s Amaury Cordeel, who suffered terminal suspension damage, with both drivers’ races ended.
Fittipaldi had qualified 14th, so will now start from 19th for Sunday’s feature race.
