The three were at 13-under-par 200 at the TPC Boston.
Stricker rolled in a 5-foot eagle putt on the last hole and finished with a 6-under 65. Goosen shot a 68 and O'Hair birdied the last hole for a 70.
Tiger Woods carded a 72 and trailed the leaders by nine strokes.
"It was tough conditions out there with the wind, not really being able to get a handle on the direction at all today, especially on that back side," Stricker said. "We were coming up short, going long. It was difficult, and the greens firmed up again today and made things a little bit more difficult trying to get them close to the holes."
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