American Rickie Fowler finished with a birdie and an eagle to push himself within three shots of the lead, alongside Charles Howell III, but Tiger Woods was tied in 32nd place, eight strokes behind the leading duo, after a third straight round of even-par 70.
Strong winds made low scores difficult. Guthrie began the day on nine-under par and shot a one-over 71 but remained with a share of the lead as only three of the top 10 players on the leaderboard broke par.
With world number one Rory McIlroy having withdrawn during the second round, citing toothache, and Woods well back, there will be no repeat of last year's final round showdown between the two most high-profile players in the game.
But a fascinating battle in tough conditions awaits.
The 23-year-old Guthrie, a US PGA Tour rookie, had three bogeys and two birdies in his round while Thompson, who has never won on the US Tour, had four birdies and four bogeys as he shot a 70.
"I'm proud of the way I played," said Guthrie, who played on the second tier Web.com tour last season while completing his degree in business management at the University of Illinois.
"I played smart, solid golf, stayed away from the trouble. Stayed to the strong side of pins, and if I missed, got it up-and-down."
Thompson earned his share of the lead with a birdie on the par-five 18th, his 21-foot putt for an eagle and the outright lead, pulling up just short.
"Hard to believe downwind, downgrain, but today was a struggle obviously," he said.
"My short game saved me; my putting saved me. I just fought through it. Just stayed positive, stayed patient, let things happen, and never got down on myself."
Ogilvy, who had not made the cut in his last four tournaments, looked far more confident with the putter as he birdied the 18th to finish with an even-par 70 after starting his round with two bogeys.
"It's hard work when you're two-over after two. That wasn't too much fun starting like that. But from five onwards, the par three, I hit it really well. I felt pretty comfortable out there," said the 2006 U.S. Open winner.
Westwood recovered from a shaky middle of his round, with bogeys on the eighth and ninth, to make his 70 with birdies on the 14th and 17th.
The Englishman, who now lives nearby the PGA National course, chipped in from the rough from 48 feet on the 14th hole.
"I normally get a bit of stick for not having a short game but I chipped inside this week and a lot of sand saves and a lot of scrambling like you need to do around this golf course. Maybe I'm turning that around," said Westwood.
South Korean Y.E. Yang, who won the tournament in 2009, was one of five players four shots off the lead after a superb bogey-free 67.
Sweden's Peter Hanson, American Keegan Bradley, England's Justin Rose and Canadian Graham DeLaet were all on four-under.
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