Stenson had seven birdies along with an eagle on the seventh hole and a lone bogey, leaving the Swede at 13-under 203 on PGA Sweden National’s Lakes Course.
Pepperell shot 65 that included eight birdies and one bogey.
Stenson is winless this year after sweeping the European Tour’s Race to Dubai and PGA Tour’s FedEx Cup last season.
“It would be huge to win at home in Sweden. I haven’t done that before so it’s something I really want to do. I’ve got a good chance, but there’s a long way to go,” Stenson said.
Stephen Gallagher (65) and Alvaro Quiros (66) are one stroke behind.
Former Augusta State golfer Scott Jamieson had 73 and is at 2-under.
CHAMPIONS TOUR: In Des Moines, Iowa, Doug Garwood shot 7-under-par 65 to take a one-stroke lead after the second round of the Principal Charity Classic.
Garwood is at 11-under 133 at Wakonda Club.
Michael Allen is second after 66. Mark Calcavecchia (69) and Tom Pernice Jr. (67) are 9-under.
Augusta native Larry Mize had 67 and is 3-under.
LPGA TOUR: In Galloway Township, N.J., Stacy Lewis moved into position to take the top spot in the world, shooting a bogey-free 8-under-par 63 for a one-stroke lead in the ShopRite LPGA Classic.
The second-ranked Lewis has a 12-under 130 total. Christina Kim is a stroke back after 67. Jennifer Johnson had 70 and is two off the lead.
A victory today would guarantee Lewis the No. 1 ranking, which Inbee Park has held for 59 consecutive weeks.