Caversham was a former United States Navy air base situated in the Swan Valley, roughly 20 kilometres north-east of Perth. It was only the third Australian Grand Prix to be held in Western Australia. The race was timed to coincide with the British Empire and Commonwealth Games in Perth, which ran from 22 November to 1 December 1962, in the hope of attracting larger crowds. Just ten cars started, with seven having made the long journey across the Nullarbor Plain from Australia's eastern states and three being local entries.
Bruce McLaren and Jack Brabham were paid appearance fees to attend and bring their current race machinery. McLaren came with a Cooper T62, fitted with a 2.7-litre Coventry Climax FPF engine. Brabham arrived with his newly constructed Brabham BT4 — the first car built by the Brabham-Tauranac combination — though his own 2.7-litre engine failed in practice, forcing him to accept a 2.5-litre spare lent by McLaren.
McLaren took pole position with a lap of 1:19.6, ahead of Brabham at 1:20.1 and Bib Stillwell's Cooper T55 Climax at 1:20.3. From the start, McLaren and Brabham ran together in a closely fought duel that continued for over forty laps, the two men already long-established rivals from Formula One and Tasman Series competition. The contest ended when Brabham, focused on McLaren while attempting to lap Arnold Glass's BRM P48, collided with Glass on lap 50 and retired. Glass survived to finish fifth.
McLaren crossed the line first in 1 hour 21 minutes 58.4 seconds, 41.6 seconds ahead of John Youl in a Cooper T55. Bib Stillwell completed the podium third, 5 seconds further back, in a season in which he had dominated the Australian Drivers' Championship — he took his first Gold Star title in 1962 and would win four consecutively through 1965. Bill Patterson finished fourth, three laps down, in an older Cooper T51. Jeff Dunkerton's ninth-place finish in a Lotus Super 7 with a 1.5-litre Ford engine was notable as the last ever classification of a sportscar in an Australian Grand Prix.
Lex Davison finished eighth in a Cooper T53, completing only 46 of 60 laps. After the race, Davison successfully negotiated to purchase Brabham's BT4 for the 1963 season.
The 1962 race marked a clear break in the character of the Australian Grand Prix. Where earlier post-war editions had often been won by gentleman amateurs driving diverse specials and modified road cars, McLaren's victory confirmed that the event now belonged to professional drivers in purpose-built mid-engine single-seaters. The contest between McLaren and Brabham — two former World Championship-level drivers from the Australasian region — gave the race a quality it had not always possessed, and their rivalry would define the Tasman Series through much of the following decade.