At the start Niki Lauda got away well from the front row and quickly pulled a lead of a few seconds, while the pole sitter Mario Andretti was dropped down to third.
But that didn't last for long, as Lauda had to pit at the end of the eight lap, but he was able to rejoin rather quickly.
Villeneuve took over the lead, only to lose it a few laps later as he ran wide at the exit of Hawthorn corner.
On lap 11 Piquet was also forced to pit in, so the leading battle was between Andretti and Villeneuve, while Jochen Mass in the Arrows had taken advantage of the pitstops and moved up to third place.
Andretti's lead was up to four seconds after Villeneuve's mistake, but the Canadian closed the gap slowly but surely.