The grandson of the late Arnold Palmer did not drop a shot at Riviera Country Club as he signed for a round of 64.
That moved him onto seven-under par and two shots clear of the chasing pack but a number of players are still to complete their first round due to the difficult conditions.
American Dustin Johnson is part of a five-way tie that are two behind Saunders, with J.T. Boston, Daniel Summerhays, Brett Stegmaier and Cameron Percy all confident of putting the leader under pressure.
There are 11 players tied in seventh on four-under par, with Jhonattan Vegas, John Huh and Jason Kokrak will be hopeful of climbing the leaderboard when they resume their first round.
World number one Jason Day and Phoenix Open champion Hideki Matsuyama have also yet to finish their first 18 holes, with play set to resume at 3pm GMT.