Price and Eger fired 6-under 66s at the Sonoma Golf Club in the final event on this year's Champions Tour to take a one-shot lead over Mike Goodes.
The tournament is limited to the top 30 players on the money list, although this year's event was reduced to 29 because Tom Watson is recovering from hip surgery.
A $1 million annuity is on the line this week as the top prize in the yearlong Charles Schwab Cup. Jay Haas went into the tournament with a 12-point lead over Fred Funk, with Bernhard Langer, Eduardo Romero and John Cook still in the running for the top spot.
Haas put himself in good position with an opening-round 69 while Funk was last after shooting a 74.
Price, a member of the Golf Hall of Fame, holed a 26-foot birdie putt at the final hole to grab a share of the lead. He has been a member of the Champions Tour for more than a year and is still seeking his first win.