Maggert shot a 65 and Fowler 66.
Watson, who has won six senior majors as well as eight on the regular tour, is aiming to become the oldest winner of the event and the oldest winner of a Champions Tour major.
The leaders have little room to breathe with Bart Bryant, Jim Carter and pre-tournament favourite Colin Montgomerie sitting just one shot back on 136.
German Bernhard Langer is part of a group of six sitting another shot away.
(Reporting by Cameron French; Editing by Peter Rutherford)
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