If the global rugby community at large felt comforted by the defeat in Melbourne on Saturday of the raging World Cup favourites, New Zealand, there was no reason for Wales to feel encouraged. The chances are that, when the World Cup begins in September, they will be vying for pride of place in group B with Australia, whose 20-15 win at the Melbourne Cricket Ground suggested a team just rediscovering their self-belief.

True, Wales will have home advantage since they play Australia on September 15 at the Millennium Stadium rather than on the soil of the host country, France, but two solid displays in the Tri-Nations tournament by the Wallabies — narrow defeat in South Africa and now victory against the All Blacks — give them a far more convincing appearance.

They have to sustain that momentum now, against the Springboks in Sydney on Saturday, probably without their veteran scrum half, George Gregan, who limped off with a damaged knee after an outstanding defensive display in Melbourne, and Wycliff Palu, the No 8. Palu has nerve damage in his shoulder and could miss the World Cup as a result, although his replacement, Stephen Hoiles, worked hard to make up for the deficiencies of his tight forwards in the scrum.

The winners of group B play the runners-up in group A in the World Cup quarter-finals, likely to be either England or South Africa, so Brian Ashton and his players, who are training in the Algarve, will monitor Australia’s development.

“We targeted this as an important match to win,” Stirling Mortlock, the Australia captain, said, “but that doesn’t change the fact the All Blacks are the team to beat at the World Cup.”

New Zealand will hope that Conrad Smith, the Wellington centre who played his first club game at the weekend after a longstanding hamstring injury, could yet play in their remaining Tri-Nations games. The midfield remains their one area of contention and Mortlock twice carved a way through it in Melbourne, creating the decisive try for Scott Staniforth.

Both Australia’s tries, in a second half that they won 14-0, came during the absence in the sin-bin of Carl Hayman, New Zealand’s loose-head prop. Even without him, Australia could exert no pressure at the scrum, but it also left the All Blacks without Jerry Collins for a five-minute period to allow on a replacement prop, weakening their defensive screen as Australia at last trusted their backs to run the ball.

Scorers: Australia: Tries: Ashley-Cooper (63min), Staniforth (72). Conversions: Giteau 2. Penalty goals: Mortlock 2 (14, 20). New Zealand: Tries: Woodcock (4), Gear (26). Conversion: Carter. Penalty goal: Carter (17).

Scoring sequence (Australia first): 0-7, 3-7, 3-10, 6-10, 6-15 (half-time), 13-15, 20-15.

Australia: J Huxley; L Tuqiri, S Mortlock, M Giteau, A Ashley-Cooper; S Larkham, G Gregan (rep: S Staniforth, 56); M Dunning (rep: A Baxter, 78), S Moore (rep: A Freier, 48), G Shepherdson, N Sharpe, D Vickerman, R Elsom (rep: M Chisholm, 71), G Smith (rep: P Waugh, 71), W Palu (rep: S Hoiles, 41).

New Zealand: M Muliaina; R Gear, L McAlister, A Mauger, J Rokocoko (rep: S Sivivatu, 76); D Carter, B Kelleher (rep: P Weepu, 51); T Woodcock (rep: N Tialata, 46), A Oliver (rep: K Mealamu, 46), C Hayman (sin-bin, 62-72), C Jack, T Flavell (rep: R Filipo, 46), J Collins (rep: Woodcock, 67-72), R McCaw, R So’oialo (rep: C Masoe, 75).

Referee: M Jonker (South Africa).

Attendance: 79,322.