Häkkinen and Coulthard started from the front row of the grid and immediately asserted a pace that would leave every other competitor lapped by the finish of the 58-lap race. Michael Schumacher, starting third for Ferrari, made a strong opening and challenged Coulthard for second before retiring on lap 6 with engine failure.
With Schumacher out, Jacques Villeneuve held third for Williams while under pressure from Giancarlo Fisichella's Benetton. After the first round of pit stops, Villeneuve fell behind teammate Heinz-Harald Frentzen, Eddie Irvine (Ferrari), and Fisichella. Fisichella moved past Frentzen for third but subsequently retired with a mechanical failure, allowing Frentzen to reclaim the position. Irvine, who had run a one-stop strategy, finished just behind Frentzen in fourth. Villeneuve, despite being lapped by the McLarens, finished fifth. Johnny Herbert scored the only championship point of his 1998 season.
On lap 36, Häkkinen unexpectedly turned into the pit lane. He drove straight through without stopping and rejoined the circuit, losing the lead to Coulthard in the process. In 2023, Häkkinen recalled: "The team said something on the radio, I was confused, I thought they asked me to come to change tyres and that was not the case. They were just giving me some different information. So I just drove through the pit lane and I of course lost the lead of the race, David got the lead." McLaren principal Ron Dennis offered a different account in 2007, claiming that an unauthorised party had tapped into the team's radio frequency and instructed Häkkinen to pit.
With 16 laps remaining, Coulthard led by 12 seconds. By lap 55 of 58, his margin had shrunk to two seconds. A few laps before the finish, Coulthard moved aside on the front straight to allow Häkkinen through to win.
The move was based on a pre-race agreement between the two drivers. Concerned about the reliability of their new car, Häkkinen and Coulthard had agreed before the start that whichever of them led at the first corner would be permitted to win the race, provided he remained in a position to do so. After Häkkinen's inadvertent pit-lane visit handed Coulthard the lead, that arrangement required Coulthard to hand the victory back.
The incident was heavily criticised and referred to the World Motorsport Council, which ruled that "any future act prejudicial to the interests of competition should be severely punished in accordance with article 151c of the International Sporting Code." Ron Walker, chairman of the Australian Grand Prix Corporation, lodged a formal complaint with the FIA over how the McLaren team's actions had determined the race outcome. Team orders remained contentious in Formula One and were formally banned following the 2002 Austrian Grand Prix, though they were subsequently reallowed after the 2010 German Grand Prix.
The victory was Bridgestone's first in Formula One following their entry into the sport in 1997 and ended a winning streak for Goodyear that had lasted since the 1991 Canadian Grand Prix. Heinz-Harald Frentzen's third place for Williams was his only podium finish of the 1998 season. Pedro Diniz's car caught fire on the way to the grid before the race.