Mickelson topped the leaderboard for most of the day and Watney took his turn alone in first place late in the day before both players fell back after double-bogeys to head into Sunday's final round knotted at eight-under-par 208.
Their fellow-American George McNeil bogeyed the 18th to fall out of a three-way tie for the lead and was alone in third place on seven-under 209.
The stumbles by the leaders brought a slew of other contenders into prime position.
Two strokes off the pace at six-under-par 210 were Britons Lee Westwood (72) and David Lynn (71), Ryan Moore (68), Australian John Senden (67), Robert Karlsson of Sweden (69) and American Derek Ernst (72).
Five players were another shot away, including world number two Rory McIlroy of Northern Ireland, who struggled with his putter on the way to posting a one-over 73 for 211.
Players will be grouped in threesomes and start earlier than usual on Sunday as forecasts call for possible heavy rains overnight that could last until Monday.
(Reporting by Larry Fine in New York,; Editing by Gene Cherry)
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