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 a 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With world number one Rory McIlroy having withdrawn during the second round, citing toothache, and Woods well back, there will be no repeat of last year's final round showdown between the two most high-profile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 PGA Tour rookie, had three bogeys and two birdies as he shot a 71 while Thompson, who has never won on the PGA Tour, had four birdies and four bogeys in a round of 70.
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.
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