Sorenstam will next meet Scotland's Mhairi McKay, who beat fellow countrywoman Catriona Matthew 1-up in round two at Sohsei Country Club in Japan.
Se Ri Pak of Korea also advanced on the strength of her 2-and-1 win over another Scot, Janice Moodie. Pak, currently second to Sorenstam on the 2001 LPGA money list, is scheduled to take on Australian Rachel Teske in Saturday's matches.
Teske was 2-down early to Aussie Wendy Doolan but evened the match by the 14th hole. Teske then won the 15th, 16th and 17th holes to post a 3-and-1 victory.
Yu-Chen Huang, the 13th-seeded player from the Japan LPGA Tour, upset No. 5 seed Kaori Harada in a 6-and-5 rout. Their second-round showdown was the only match to pit two players from the host JLPGA against each other.
Thursday's opening round featured 16 matches between LPGA Tour members and JLPGA players. LPGA players captured 12 of the matches on the first day and six of those winners moved on with victories Friday.
The only other golfer from the JLPGA to advance to the quarterfinals was Aki Takamura, who downed the LPGA's Jill McGill 1-up. Takamura will face Huang on Saturday.
Sorenstam took control of her match versus Redman by birdieing the first hole with a 10-foot putt before winning four straight holes, starting at the fifth. After the pair halved six holes in a row, Sorenstam closed things out with a par to Redman's bogey at the 15th.
'I was very fortunate to get off to a good start and it was a good frame of mind to start in,' said the Swede, who is seeking her seventh title of the year. 'I think in match play it is important to get off to a good start because you have the advantage right away over your opponent.'
Although Pak was 3-up after eight holes Moodie managed to cut into her lead with wins at the 10th and 12th. Pak claimed the 14th and three halved holes later, the match was over.
'I am hitting the ball well and that is giving me the opportunity to play well,' said Pak, who has six top-three finishes in her last seven starts, including three victories.
In other action, Canada's Lorie Kane notched wins at the first three holes Friday on her way to a 3-and-2 triumph over Kaori Higo of the JLPGA. Kane's next opponent will be Emilee Klein, a 1-up winner over England's Laura Davies in round two.
Full-field scores from the CISCO World Ladies Match Play Championship