Two David Pocock tries saw Australia to a hard-fought 28-13 victory over Fiji in their World Cup opener on Wednesday night, but they failed to drive home their advantage to get a crucial bonus point.

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Victory at Cardiff’s Millennium Stadium left two-time champions Australia third in Pool A behind England and Wales. Their rivals have both bagged bonus points for scoring four tries or more on the opening weekend

. Australia captain Stephen Moore said: “I thought Fiji were terrific – they’re a much-improved side. We’re happy with our efforts, but there’s plenty to work on for the next Test.”

Coach Michael Cheika played down the importance of the bonus point.

“We haven’t thought about the bonus point. It’s not Super Rugby, it’s the World Cup.”

Twice in four minutes, Pocock was driven over by the Wallabies’ effective rolling maul after they spurned kicks at goal in favour of attacking line-outs.

Prop Sekope Kepu crossed for a third try early in the second half, with fly-half Bernard Foley kicking 13 points. But Fiji defied fears that they would give up.

Taking to the field just five days after a 35-11 defeat by England in the tournament opener, the Pacific islanders scored a try through Australian-born fly-half Ben Volavola, with giant wing Nemani Nadolo kicking the conversion and two penalties.

Australia pinned Fiji back in their half for the opening 10 minutes, but a few forced final passes saw the Wallabies only bag a Foley penalty for their dominance after the islanders strayed offside.

The next 10 minutes saw a reversal of fortunes. An attempted Wallaby push-on in the scrum backfired as the Fijians locked in, held the push and countered with one of their own.

A kick to the corner from the resulting penalty saw Fiji launch a line-out drive, Scott Fardy straying offside and Nadolo eventually kicking the penalty in front of the posts to draw the teams level.

Live-wire scrum-half Nikola Matawalu was at the centre of all Fiji did, but his ruck infringement and then a Nadolo high tackle on Israel Folau saw Pocock driven over after the Wallabies again ignored a kickable chance in favour of an attacking line-out.

Fiji suffered a hammer-blow when Campese Ma’afu was yellow carded on the half-hour after preventing quick ball for the Australians. Foley again kicked for the corner and Pocock bagged his second try after a perfectly executed rolling maul trundled over the whitewash.

Wallaby No 10 Foley kicked his second penalty just before halftime, and Australia started the second period in ideal fashion, Folau punching holes down the left before the ball was worked to Kepu in midfield, the tighthead prop barging over from close range for a try Foley converted.

Nadolo responded with his second penalty and Fiji then decided to run everything, with mixed results in the face of their own inaccuracy and a doughty Wallaby defence.

Fiji finally broke the Australia line when Volavola, the Sydney-born former Australian Under-20 player who has signed for the Crusaders next season, dummied past Rob Simmons and rolled out of Foley’s attempted tackle for a try converted by Nadolo.

Foley kicked his third penalty in the 70th minute, and then Fijiborn Wallaby centre Tevita Kuridrani was yellow carded with seven minutes to play after infringing in a tackle on his cousin Nadolo.