Matthew eagled two holes on the back nine en route to a 6-under-par 66 and Lincicome shot a 71. Both were at 5-under 211, taking a one-stroke lead into the final round of the Ladies European Tour event.
Sorenstam, the three-time defending champion, shot a 74 and was at 4-over 220. She hit only three fairways and missed her few birdie chances.
'This is my toughest time as a golfer. ... I have felt better,' she said.
The 36-year-old Swede is heading toward her most disappointing season. She had a second place-finish in March, then didn't make the top 10 again until July. She hurt her back in April and was sidelined for two months.
The winner of 10 majors and 84 tournaments worldwide, Sorenstam has not made a birdie in the last two rounds on the course where she helped Europe win the 2003 Solheim Cup against the U.S.
Sweden's Louise Stahle had a 69 and was at 212. Norway's Suzann Pettersen, who won her first major this year at the LPGA Championship, shot 70 and was another stroke behind.
Laura Diaz of the U.S., the second-round leader, slipped to a 75 and was at 214 with Swedes Sophie Gustafson, Maria Hjorth and amateur Caroline Hedwall.
Matthew is playing only her third European tour event of the year after becoming a mother in December. Her eagles came on the 12th and 16th, two of the shortest par-5s on the Barseback course. On the 12th, Matthew came close to her first double eagle, hitting a 7-iron approach that landed a foot from the hole.
'I hit a lot of greens, and obviously two eagles on the back nine helped my score a bit,' Matthew said. 'So I'm pleased with how I played.'