Allenby, who said inflammation in his right hand was so bad four days ago that he could hardly pick up a club, finished just minutes after 21-year-old American Spencer Levin finished with an 8-under 64.
Levin was in second place at Moonah Links, followed by Australia's Scott Laycott at 7 under. Adam Scott and Geoff Ogilvy were tied for fourth a stroke back.
Two-time winner Aaron Baddeley and Stuart Appleby both had 70s and a share of 16th place at 2 under.
Allenby, the 1994 Australian Open champion, had 10 birdies and a bogey and said he hadn't putted better in a decade. He played in the same group as Mark Hensby, who on Wednesday criticized former No. 1 Greg Norman for not doing enough to support golf in Australia. Hensby shot a 71.
'On Monday, at lunchtime, I couldn't hold a golf club,' said Allenby, claiming he was only able to play after several sessions of physiotherapy and still wasn't sure he could finish the tournament.
'I could do one thing wrong and be walking back to the clubhouse,' he said. Allenby hurt his hand three weeks ago and had to withdraw from a tournament in the United States last week.
Defending champion Peter Lonard, aiming for his third consecutive Australian Open title, opened with a 2-over-par 74.
The tournament started amid concerns over the shrinking size of the Australasian tour and Hensby's comments about Norman.
Norman, voted Australia's golfer of the 20th century, said he was shocked by Hensby's comments and had spoken to the U.S. PGA Tour player by telephone.
'No, everything is not fine. We're not finished (with) the conversation,' Norman said Thursday. 'I don't have to go out there and play golf tournaments every week in this country. We do a lot of things behind the scenes that a lot of people never see, and I think that's something Mark Hensby will never know because he doesn't know me.'
Norman isn't playing any tournaments this season on the Australasian Tour, which has been cut to six tournaments -- and three of those are jointly sanctioned.
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