'There are just so many great things that go along with winning,' said Funk. 'And there just aren't that many good things, except the money, that go along with finishing second.'
Steve Lowery and Skip Kendall each posted 72-hole totals of 266 in 2000 when the course played as a par-72. Dan Halldorson posted a total of 263 in 1986 when the course was a par-70.
Palmer closed with an 8-under 64 to take second place at 21-under-par 267. Glen Day, J.J. Henry, Kevin Na and Loren Roberts were one stroke further back at minus-20.
Funk climbed into the lead Saturday with a 64 and needed every birdie he could get on Sunday. After parring the first two holes at Annandale Golf Club, Funk had already fallen out of the lead as several players went flying past him.
The University of Maryland graduate dropped in his first birdie at the third. Funk came back with a birdie at the par-5 fifth to get to minus-18. He garnered his third birdie at the seventh.
Funk, however, stumbled to a bogey at the eighth. He atoned for that mistake with a birdie at the 11th. The six-time winner on the PGA Tour converted a birdie at the par-3 15th.
He came right back with a birdie at 16 to join Palmer, who was done his round, atop the leaderboard with two holes to go. Funk parred the 17th and it came down to the par-5 closing hole.
Funk managed a two-putt birdie at the last to pass Palmer and win for the first time since the 1998 Deposit Guaranty Golf Classic.
'It's been a long, long road since 1998,' Funk said. 'I had 22 under as my target score. I figured somebody would get to 21 under for sure.'
Palmer looked well on this way to his first PGA Tour win, but tripped to a pair of back-nine birdies to fall one shot short. He opened with a birdie at the first to get to minus-14.
The 28-year-old ran off four consecutive birdies from the par-5 fifth. Palmer picked up his sixth birdie at the 10th to move to 19 under. He climbed to minus-20 with a birdie at the 12th.
Palmer ran into trouble with a bogey at the 13th. He bounced back to birdie 14, but again faltered to a bogey at the 15th. He responded with a birdie on 16 and another on 18, but the bogeys cost him a chance at his first PGA Tour title.
Kirk Triplett closed with a 66 to end at 19-under-par 269. Jonathan Byrd and Tim Clark shared eighth place at minus-18. Pat Bates, Greg Chalmers, Chris Couch and Carl Pettersson were one stroke further back at 17-under-par 271.