Alonso's Renault, which started from pole, led until half-distance, and Ferrari had to employ unconventional tactics to get ahead during pit stops.

Schumacher's extra pace secured him the win despite making one more stop.

Rubens Barrichello was third, while Jarno Trulli, Jenson Button and David Coulthard completed the top six.

Schumacher always had marginally the faster car, but Ferrari decided they would not beat Alonso if they stayed on the same strategy.

So they decided to go for a fourth stop and use the extra grip afforded him by a lighter fuel load and softer tyres to lap at the extra speed he needed to beat the Renault.

Alonso was struggling for grip when Schumacher made his second stop on lap 29, and his only chance to hold off the Ferrari was to stop on the next lap.

Instead, Renault waited three laps, which gave Schumacher time to lap at record pace and make up the time he needed to ensure he was ahead by the time Alonso stopped on lap 32.

Ferrari had further gambled by adding very little fuel to Schumacher's car at that stop in a bid to get in some very fast laps and further extend his advantage.

Despite losing the lead when he made his third stop on lap 42, he had lapped more than fast enough to regain it when Alonso stopped on lap 48.

Schumacher's extra pace then ensured he had a few seconds in hand when he made his final stop on lap 58, 12 laps from the end of the race.

It was a race in the fashion of Schumacher's brilliant tactical victory over the McLarens of Mika Hakkinen and David Coulthard in the 1998 Hungarian Grand Prix.

"After the second pit stop we decided to go for a four-stop strategy," said Schumacher.

"It was just brilliant. The guys have just done fantastic pit stops, very precise.

"I wasn't really so optimistic going into the race. There was no risk of falling back, just the opportunity to go forwards - and we did it."

Schumacher and Alonso fought a private battle at the front of the field, with no-one else able to get near them.

Trulli catapulted up from fifth on the grid with a superb start to be third by the first corner on lap one.

The Italian, who won in Monaco in May, came under threat from Button and Barrichello from about half-distance, and held them off until the penultimate corner, when Barrichello slipped through.

The Brazilian had earlier passed Button just after their third and final pit stops.

The Englishman came out of the pits just behind Trulli, with Barrichello right behind the BAR.

The Brazilian seized his opportunity to pass into the Adelaide hairpin while Button was concentrating on the Renault.

Coulthard dropped down from third on the grid in McLaren's new car to be fifth after the first lap.

The Scot could not quite match the pace of those in front of him, but was comfortably able to hold off team-mate Kimi Raikkonen, who finished one place behind him.

Juan Pablo Montoya was a disappointing eighth in the first race for Williams' heavily revised car.