Ginn, the 2002 Ford Senior Players Championship winner, stands at 3-under-par 210 after three rounds. The win at the Senior Players is Ginn's only Champions Tour title.
Tom Watson, who won the 1980 British Open at Muirfield, managed a 1-under 70. He stands at 2-under-par 211 after three rounds and is the only player with three rounds of par or better.
Mark O'Meara, the 1998 British Open champ, also shot 70 and is alone in third at even-par 213. Eduardo Romero, who won the JELD-WEN Tradition last year, is in fourth at plus-1 after a 2-over 73 Saturday.
Ginn got off to a tough start with bogeys on one and two, dropping him to plus-1. He recovered one of those lost strokes as he birdied the par-5 fifth.
The 58-year-old Ginn moved back to minus-1 and a share of the lead when he birdied the eighth. He parred six in a row around the turn.
Ginn converted a 15-foot birdie effort on the par-4 15th to grab the out-right lead. He came right back to birdie the 16th for the second straight day, then parred the final two holes to get in a minus-3.
Watson, a five-time British Open and two-time Senior British Open champion, also tripped to a bogey on the first. He recovered that lost stroke with his second birdie in two days at the par-3 seventh.
After three straight pars around the turn, Watson faltered to a bogey on the par-4 11th. He atoned for that error with a birdie at the 13th.
Watson knocked his third to 2 feet and knocked that putt in for birdie at the par-5 17th to get to 2 under before he parred the last. Watson has played No. 17 to 4 under through three rounds.
Sam Torrance, the 2003 European Ryder Cup captain, carded an even-par 71 and completed three rounds at 2-over-par 215. He was joined there by Morris Hatalsky, Gordon Brand, Jr. and Donnie Hammond.
Dave Stockton, one of the first-round co-leaders, shares ninth with Senior PGA Championship winner Denis Watson.
Ireland's Des Smyth, who led entering the third round, struggled to a 6-over 77. His round included two birdies, a double-bogey and six bogeys. He shares 11th with defending champion Loren Roberts, Nick Faldo and two others.