The pair carded four-under par rounds of 66 to take the clubhouse lead before a tornado warning and heavy rain saw 56 players forced off the course before they had completed their opening rounds.
South Korea's Amy Yang was one shot back, with 2012 winner Choi Na-yeon and American Jane Park also on three-under, having completed 15 and 12 holes respectively.
A group of eight players, which includes world number one Inbee Park and American Morgan Pressel, find themselves at two-under. Park still has four holes of her round to complete.
Seven-time major winner Webb is looking for her first major title in nine years, and began her quest for victory in solid fashion. The Australian found every fairway and 17 out of 18 greens.
Having begun on the 10th tee, Webb rolled out nine consecutive pars before a birdie run on her closing nine saw her rise to four-under.
Alex, who has never led an LPGA round, produced five birdies in her round of 66, with a bogey at the 18th her lone blemish of the day.
Park birdied two of her last three holes to move towards the top of the leaderboard, with the South Korean in a strong position with four holes still to play.
Last year's runner-up, Stacey Lewis, is at one-under after a round of 69, while world number two Lydia Ko made a solid yet unspectacular start to her bid for a first major title, firing an opening 70.
Defending champion Michelle Wie is currently in a tie for 62nd after carding a two-over 72.