Stuart Appleby (64) and Tim Petrovic (65) share third place at 15-under-par 201. Chris DiMarco, the 2000 champion, shot a 67 in Sunday's third round and is tied for fifth place with Frank Lickliter (65) and Rory Sabbatini (64) at minus-14.
Golfers are playing 36 holes on Sunday to complete the 72-hole tournament after play was canceled Friday due to the effects of Hurricane Isabel. Players had about 20 minutes between the third round and their tee times for the final round.
Beckman mixed in two birdies and a bogey on his front nine but ascended to the top of the leaderboard with his play on the back nine at the Mystic Rock Course at Nemacolin Woodlands Resort & Spa.
He tallied three birdies in a row from the 11th and did it again from the 16th to close out his 64.
Craig Barlow (68), Carl Paulson (66) and David Peoples (67) share eighth place at 13-under-par 203.
Ben Curtis, the reigning British Open champion, shot a third-round 70 and is part of a group tied for 20th place at 10-under-par 205.