The aircraft was operating as Qantas Flight QF36 and was approaching Melbourne at the end of a flight from Christchurch, New Zealand. Air Traffic Control of the aircraft was being exercised by Melbourne Approach, which was directing the aircraft for a landing on Runway 27 at Tullamarine. While the aircraft was on track from Wonthaggi towards a radio beacon at Epping, the controller gave vectors to shorten the distance to run to Tullamarine. This track shortening, using radar, is a standard technique, used to aid separation with other aircraft and to provide a smooth flow of traffic. The controller obtained approval from the Essendon controllers to vector QF36 through Essendon airspace. The aircraft was progressively descended and when clearing the aircraft to descend to 2000 feet the controller advised the crew that the aircraft was 4 miles to the left of the runway extended centre line. The crew advised that they had visual contact with the ground and were then cleared to continue a visual approach. Shortly afterwards, the crew sighted a runway and commenced a turn to the left, during which visibility reduced as the aircraft entered a rain shower. On passing through the shower, the crew immediately realised that they had turned towards Essendon, and a right turn was carried out to continue tracking towards Tullamarine. When the premature turn was commenced, it was observed on radar by the Approach controller and visually by both the Melbourne and Essendon Tower controllers. The Approach controller queried the aircraft intentions at about the same time as the crew commenced the turn back towards Tullamarine. A normal landing was carried out about 3 minutes later. During the excursion from the expected track, the aircraft descended to a height of about 1300 feet above the ground. There was no possibility of the aircraft landing at Essendon, as a transfer to Tower frequency had not been made and consequently no landing clearance had been provided. The elapsed time from the start of the left turn to the turn back to the right was about one minute. Safety of operation was not jeopardised at any stage, and the occurrence was not regarded as an air safety incident.