The only changes to the driver lineup from the field in South Africa a month earlier were because of injury: Stephen South was in the second McLaren in place of Alain Prost (who had a broken wrist) while Jan Lammers was again in the ATS. This was the sensation of qualifying as the Dutchman set the fourth fastest time with the new D4 chassis. Pole position went to Nelson Piquet in the Brabham ahead of René Arnoux's Renault and Patrick Depailler's Alfa Romeo. Alan Jones was fifth in his Williams with Bruno Giacomelli sixth in the second Alfa. Then came Carlos Reutemann (Williams), Riccardo Patrese (Arrows), Didier Pironi (Ligier) and Gilles Villeneuve in the Ferrari. Jacques Laffite was a disappointing 13th while World Champion Jody Scheckter was a dismal 16th in his Ferrari.

At the start Piquet managed to get to the first corner just ahead of Arnoux with Depailler third and then Lammers, Jones and Giacomelli three abreast. Behind then Mario Andretti's Lotus ran into the back of Jean-Pierre Jarier's Tyrrell, an accident which caused Zunino to crash. Moments later Lammers's race ended with a driveshaft failure.

This left Piquet, Arnoux and Depailler ahead of Jones, Giacomelli and Patrese. Depailler and Jones were soon ahead of Arnoux and Patrese dropped behind Reutemann but on the fourth lap there were a series of accidents as a result of Giacomelli spinning. Jarier and Reutemann were both eliminated while the promising Elio de Angelis (Lotus) crashed into the rear of Eddie Cheever's Osella and injured his ankle.

Piquet was able to edge away from Depailler with Jones, Arnoux and Patrese chasing. There was then a gap back to Villeneuve and the other midfield survivors. It took Jones until the 18th lap to get into second place while further back Villeneuve had moved up to fourth by overtaking Patrese and Arnoux. Patrese soon followed to get ahead of the Renault, while Villeneuve worked his way past Depailler. The Frenchman's race ended with a rear suspension failure on lap 41 and soon afterwards Villeneuve dropped back after damaging the nose of his car as he lapped Derek Daly.

A lap later Jones disappeared when he collided with Giacomelli, who was a lap behind. All this meant that Piquet was well ahead of Patrese while Arnoux was dropping back towards the Ensign of Clay Regazzoni. Unfortunately on lap 51 Regazzoni the Ensign suffered a brake failure and crashed into Zunino's abandoned Brabham. It then flew through the air and hit a concrete barrier. Regazzoni suffered spinal injuries.

Piquet duly won his first Grand Prix victory with Patrese second and Emerson Fittipaldi third.