Piquet suffered a last-lap engine failure which dropped him from third to sixth, giving Reutemann a three-point lead in the championship with two races remaining.
Alan Jones in the other Williams and Nelson Piquet in the Brabham made up the third row, and the top ten was completed by John Watson in the McLaren, Didier Pironi and Gilles Villeneuve in the two Ferraris, and Bruno Giacomelli in the Alfa Romeo.
Teammate Derek Warwick failed to qualify along with Marc Surer in the Theodore, Beppe Gabbiani in the Osella, Siegfried Stohr in the Arrows, and Keke Rosberg and Chico Serra in the two Fittipaldis.
On the run-up to the first chicane, Prost passed both Reutemann and teammate Arnoux to take the lead, while Pironi jumped from eighth to fourth.
As Prost cruised to victory, ultimately finishing some 22 seconds ahead of Jones, Piquet looked set to hold off championship rival Reutemann for third, until his engine blew on the last lap.
Reutemann thus led the Drivers' Championship by three points from Piquet with two races remaining, with Prost, Jones and Laffite all retaining outside chances of the title.