Beem started slowly at Victoria Golf Club with a birdie and a bogey through his first three holes, but birdied the fifth to reach 5-under par. He birdied the last two holes on the front side to make the turn at 3-under 31 and get to 7-under for the tournament.
He parred the first five holes on the second nine before closing with three birdies in his last four holes to grab a share of the lead.
'I'm starting to get the hang of the greens,' said Beem, who needed only 26 putts on Saturday. 'It's a really fun golf course and it lends itself to good scoring.'
Allan, who made 16 cuts in 30 starts on the PGA Tour in 2002, collected four birdies in his first 10 holes. He drained a 35-foot eagle putt at the par-5 18th to match Beem at the top of the leaderboard.
'I felt my odds here were way too high,' said Allan, who hit 16 of 18 greens in regulation on Saturday. 'I know this place too well. I've really been playing well, but I just haven't been putting four rounds together.'
Allan will not have to worry about stringing four rounds together as the tournament was reduced to 54 holes. Unplayable greens forced tournament officials to abandon play on Thursday and the decision was made on Friday to trim the tournament to three rounds.
Gavin Coles is alone in fifth place at 8-under par, followed by Australian Adam Scott, who is alone in sixth place at minus-7.
Scott, who shot a 64 on Saturday, has never won in his home country of Australia but seems confident that it will happen.
'I'll know I'll win in Australia. It's a matter of time,' said Scott, a two-time winner on the European Tour in 2002. 'I feel I can relax a bit more playing in Australia at the end of a long year.'
Aaron Baddeley, a two-time Australian Open champion, carded a 6-under 64 on Saturday to finish alone in seventh place at 6-under-par 134.
Stuart Appleby, the 2001 champion, is tied for eighth with Adam Crawford, Jason King and Wayne Grady at 5-under-par 135.