The 61-year-old Simson, the 2010 winner from Raleigh, N.C., beat Jim Knoll of Sunnyvale, Calif., 3 and 2 in the semifinals.
"I have about another 15 minutes to celebrate and then I have to get ready for tomorrow," said Simson, who grew up in nearby Chatham. "I had it going today. I knew I was going to have a tough match with Jim and I just can't get over some of the things I did out there. I think I hit every fairway and every green."
The 55-year-old Skinner, from Lake Bluff, Ill., edged Douglas Hanzel, of Savannah, Ga., 2 and 1.
"My intent was to make the cut and win one match," said Skinner, making his first appearance in the event for players 55 and older. "I've been in a couple of absolute dogfights and I am happy to come out ahead."
In the morning quarterfinals, Simson led Stephen Sharpe, of Greensboro, N.C., 5 up after 10 holes when Sharpe conceded the match following a rain delay. Skinner beat Steve Golliher, of Knoxville, Tenn., 2 and 1.
Skinner also finished off his suspended third-round match, beating Canada's Graham Cooke in 19 holes.