Eaks shot a 2-under 70, while Mark McNulty (66) and Mike Reid (70) are knotted in third place at minus-4.
Arnold Palmer, who is believed to be playing his last competitive round in his hometown, struggled to a 14-over 86 and is toward the bottom of the leaderboard.
'The local people have, for all my life, been extremely supportive of me and my golf,' said Palmer, who is building a house near Laurel Valley. 'What can you say after you shoot the kind of scores I shot? I did play one good hole and that was it. So that gives me a license to play another round some time.'
Now that Palmer completed his two rounds, the focus shifts back to the tournament and Pate, who is searching for his first win on the Champions Tour since joining the circuit last year.
Pate began on the back nine Friday and bogeyed the 12th when he three-putted from 45 feet. He reclaimed the lost stroke at the 15th, but it didn't look like a birdie was coming. Pate drove into a bunker, then hit a 7-iron to 60 feet, where he sank the birdie putt. He made it two in a row with another long putt, but found trouble at the par-5 18th.
His drive landed in the fairway, but he hit a 4-iron into the wind from 175 yards. Pate hit 'absolutely the worst shot I think I've ever hit in my professional career' and came up short of the lake. His third went through the green and he walked off with a bogey.
Pate calmed down on his second nine and rolled in an 8-foot birdie putt at the third. He reached the green in two at the par-5 sixth and left his 30-foot eagle putt on the edge. He tapped in and kicked off a run of golf that jumped him to the top of the leaderboard.
At the seventh, Pate hit a 9-iron 20 feet short of the hole and converted the birdie putt. He birdied the difficult, par-3 eighth to reach 6 under par and take the lead.
'The golf course played difficult if you didn't hit good shots and if you hit good shots, there were holes you could make birdies on,' said Pate, who won the 1976 U.S. Open. 'I've been the leader in enough tournaments to know you got to play one shot at a time.'
Pate has not won since the 1982 Players Championship, but has been close on the Champions Tour. He has nine top-10s on the 50-and-over tour, including two this year, and is ready to return to the winner's circle.
'Although I haven't been in the lead in a long time it's still the same game,' said Pate. 'It's the same process. Just have to play your game. And for me I have to be patient and calm and swing slow.'
Eaks played poorly to start his round with four bogeys in his first five holes. He drew even on his round with four birdies in a five-hole span from the sixth, then played smart golf down the stretch to grab second place.
At the 15th, a hole he bogeyed on Thursday, Eaks hit a 9-iron to 15 feet and drained the birdie putt. He polished off his round of 70 with a birdie at the last.
'Overall I'm pleased as punch with that round,' said Eaks, a three-time winner on the Nationwide Tour. 'That was a good comeback. Stuck in there and at least I got it setup for the weekend.'
Dave Barr (72), Tom McKnight (72) and Hajime Meshiai (71) are tied for fifth place at 3-under-par 141.
First-round leader Graham Marsh (74), 1995 champion Ray Floyd (72), reigning U.S. Senior Open champion Peter Jacobsen (71) and MasterCard Championship winner Dana Quigley (71) share eighth at minus-2.
Defending champion and four-time winner Hale Irwin dropped four shots over his last six holes to shoot a 3-over 75. He is part of a group tied for 13th at even-par 144 that includes Tom Kite, Mark James and Tom Purtzer.
The 36-hole cut fell at 6-over-par 150 and among the notable players who will be absent on the weekend are: Jay Haas (151), 2003 winner John Jacobs (153), Gary Player (155) and 2002 champion Fuzzy Zoeller (155).