Moore, 57, won the first hole and never fell behind in the match, taking a 4-up lead through nine holes and clinching the win with a par at the 13th.
'I played about the same as I did on (Sunday),' said Moore. 'Fran got in the rough a few too many times. That made it a little easier for me.'
Moore claimed medalist honors on Sunday by one shot.
'Don't think I wasn't thinking about the medalist kiss of death type of thing,' she said. 'I didn't want to go out in the first round. It was in the back of my mind.'
Carol Semple Thompson, a four-time Senior Women's Amateur winner, was among three previous champions who won afternoon matches. She knocked off Kathleen Hunt, 3 and 2.
Two-time defending champion Diane Lang defeated Linda Maynard, 4 and 2, to keep alive her chance of a three-peat, while past winner Carolyn Creekmore was also a winner.
There will be two rounds of match play on both Tuesday and Wednesday. The 18- hole final is scheduled for Thursday.