Clagett, 59, collected seven birdies with just one dropped shot and holds a two-stroke lead at the Farm Club. He tied the record set by Bob Kulp in the first round in 2003.
'I got away with a couple of mistakes because you can't play this golf course without mistakes,' said Clagett of the 6,737-yard, par-72 track. 'On a golf course like this that puts a premium on shot-making, you are going to make mistakes. To shoot four-, 5- or 6-under-par, you're very fortunate.'
Clagett, who is playing in his third Senior Amateur, began on the back nine and made the turn at minus-1. But he scorched the front nine with a 5-under-par 31 to finish his round.
'Good God, I made five birdies on my back nine with 13 putts,' Clagett exclaimed. 'Where am I going with that? That's pretty good.'
John DiMuccio played through an arthritic back and hit every fairway and all 18 greens in regulation to end alone in second place at 4-under 68.
'It was good day,' said the 56-year-old, who joked that he needed 'only seven or eight Advil' to play through the pain. 'That's as good as I've played, ever. It's got to be.'
Randy Reifers, 59, is one stroke further back in third.
Greg Reynolds, the 2002 winner, shares fourth place with five other players after an opening-round, 2-under 70. Reigning British Senior Amateur champion Alan Foster is also at minus-2.
Defending champion Mark Bemowski, who lost to Reynolds in the 2002 final before beating him last year, leads a group of seven players tied for 10th place at one-under. Danny Yates, the 1992 Mid-Amateur champion, is also there.
'The first round is so important,' Bemowski acknowledged. 'You just cruise right through, get some practice and go again. I feel good.'
All in all, there are 24 players even-par or better after the first round.