The 68 by Allen, a senior at Cal State-Northridge who won the Big West Conference tournament last month, was her lowest competitive round.
Tina Miller, the Big East tournament co-champion from Miami, was two shots behind Allen.
Wie got off to a quick start, launching a 310-yard drive on the par-5 10th hole to set up a two-putt birdie, then added birdies at Nos. 11 and 14 to go to 3-under through five holes at Ocean Hammock Golf Club.
However, she three-putted for bogey at No. 17, double bogeyed No. 18 after driving the ball near a bush on the right of the fairway, and double bogeyed No. 5 after hitting her tee shot in the water.
Wie recovered with a birdie and three pars, making a six-foot putt to save par at her last hole, the par-4 ninth.
Wie finished tied for ninth in the Nabisco Championship, the LPGA Tour's first major this year.
She is playing in the Public Links for the fourth time, having first qualified at the age of 10 in 1999. She already has qualified to play in the U.S. Women's Open, the U.S. Women's Amateur and the U.S. Girls Junior, all later this summer, and has played in two LPGA events.
'People expect a lot of me, but I'm not really listening to that,' Wie said. 'I expect more out of myself than they could.'
Allen birdied the four par-5s, ranging from a three-inch putt at No. 6 to an 18-footer off the fringe at No. 10.
The top 64 players after Wednesday's final round of stroke play will advance to first round of match play Thursday.
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