Funk finished with a 2-under 69 and took the title at 12-under-par 201. Beck, also searching for his maiden win on the elder circuit, fired a 6-under 65 to finish one back at minus-11.
Scott Simpson posted a 2-under 69 at Oak Hills Golf Club for third place at minus-10.
Two-time Masters champion Ben Crenshaw matched his best finish on the Champions Tour Sunday. He carded a 3-under 68 and tied for fourth place with Loren Roberts (69) and Raymond Floyd (71) at 8-under-par 205.
Funk began the final round with a one-shot lead over Floyd and the 2005 Players Champion struggled badly at the outset. Funk bogeyed one and two to fall behind the lead and after he traded a birdie and bogey at six and eight, he needed a strong run to get back into the lead.
At this point Beck moved into the lead thanks to a strong front nine. Beck birdied, one, five, eight, 10 and 12 to move two clear of Funk at 10 under par.
Funk two-putted for birdie from close to 40 feet at the 10th, but still trailed Beck by two. At the par-3 13th, Funk's tee ball found a greenside bunker, but the 50-year-old holed out from the trap to cut the margin to a shot.
Funk bogeyed the 14th, but got the stroke back with a birdie at 15. He drained a 10-foot birdie putt to pull even with Beck at the 16th, then moved ahead with a 12-footer for birdie at 17.
At the par-3 closing hole, Funk had a long way to go, but lagged his birdie putt to a foot. He tapped in to secure the win and become the youngest champion of this event.
Mark McNulty (68), Ron Streck (71), R.W. Eaks (71) and defending champion Jay Haas (72) tied for seventh place at minus-7.
Haas is the leading money winner on the Champions Tour and despite finishing lower than the man in second place on the money list, Roberts, is still ahead with next week's season-ending Charles Schwab Cup Championship, reserved for the top 30 on the money list.