Svoboda has already wrapped up a PGA Tour card by finishing 25th on the Web.com money list. Peterson was 30th on the Web.com money list.
Peterson had five back-nine birdies to shoot 5-under-par 67 to match Svoboda at 10-under 206 at River Run. Svoboda had 69.
Taylor, who missed the cut in the first event of the Finals series, shot 70 on Saturday and is tied for sixth place, three shots off the lead. He had been tied for ninth place after two rounds.
The bulk of the field is made up of players in the top 75 on the Web.com Tour money list and Nos. 126-200 in the PGA Tour’s FedEx Cup standings. The top 25 on the Web.com money list are assured PGA Tour cards, while the other players are fighting for 25 additional cards through earnings in the four-event series.
CHAMPIONS TOUR: In Sainte-Julie, Quebec, Bernhard Langer shot 5-under-par 67 to open a three-stroke lead in the Montreal Championship.
Kenny Perry is 3-under along with Willie Wood, Chien Soon Lu, Bill Glasson and Anders Forsbrand. Perry had 71, Wood and Lu shot 68, and Glasson and Forsbrand shot 69.
EUROPEAN TOUR: In Crans-Sur-Sierre, Switzerland, Craig Lee shot 10-under-par 61 to surge into a two-shot lead after the third round of the European Masters.
Thomas Bjorn, Alejandro Canizares and Victor Dubuisson are tied for second.
WALKER CUP: In Southampton, N.Y., NCAA champion Max Homa beat Max Orrin 5 and 3 and the United States won the first six singles matches in the Walker Cup to take an 8-4 lead over Britain and Ireland at National Golf Links of America.
The U.S. rallied after Britain and Ireland took a 2½-1½ lead in the morning foursomes matches.