The 51-year-old Donnelley, who waited until Monday morning to claim her victory after stroke play was suspended Sunday night, rolled to a 4 and 3 victory over Nancy Chaffee.
Carol Semple Thompson and Carolyn Creekmore, who finished five strokes adrift of Donnelley's six-over-par 150 total in stroke play, also won in match play Monday.
Semple Thompson beat Cheryl Brayman 5 and 3 and Creekmore battled Jill Christiansen for a 2 and 1 victory. Martha Lang, who was fourth in stroke play, defeated Therese Quinn 2 and 1 on Monday.
The second and third rounds of match play are scheduled for Tuesday. The quarterfinals and semifinals are slated for Wednesday, with the 18-hole final to be played on Thursday.
The Senior Women's Amateur is one of 13 national championships conducted annually by the United States Golf Association, 10 of which are strictly for amateurs.