That left her two strokes clear of American rookie Annie Park and Australia's Minjee Lee, with Mexico's Alejandra Llaneza a further shot back after carding a six-birdie 68.
Morgan Pressel, who won her first major title at the 2007 ANA Inspiration, opened with a 69 while fellow American Stacy Lewis, the world number four and the Yokohama Tire LPGA Classic champion in 2012, returned a 71.
Beck, who has never recorded a top-10 finish on the LPGA Tour and has missed six cuts in eight starts this season, was delighted to be rewarded for a lot of recent hard work.
"I was doing well and making putts, even though I did miss some birdie opportunities," Beck told reporters after totalling only 26 putts. "But I made good putts for birdies and just kept going.
"I have been working on my swing in the past month or so. Struggled a bit after Australia but last week my game started feeling better," the Israeli, whose best finish this season was a tie for 27th at the Kia Classic in March, told lpga.com.
"I need to play relaxed golf and not put too much pressure on myself. Keep enjoying the experience and continue focusing on making birdies."
Pressel, who cooled off after a red-hot start highlighted by four birdies in her first five holes, was stunned when she saw that Beck had carded a 65.
"Laetitia, seven under out there! What an incredible score!” the 27-year-old American told Golf Channel. "That's pretty good out here. The wind played really tough and it was tough to get it close to the hole."
(Reporting by Mark Lamport-Stokes in Los Angeles; Editing by Frank Pingue)
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