Sorenstam, who served as host for this event, needed those final three birdies to fend off world No. 2 Lorena Ochoa. Sorenstam's 65 matched the course record that Ochoa set on Friday.
The Mexican was 5-under par over her final nine holes, but ended one stroke back at minus-20. Ochoa closed with a 7-under 66 on the par-73 Bro Balsta Golf Club.
Suzann Pettersen carded a 5-under 68 to end alone in third at 16-under-par 276. Gwladys Nocera took fourth at minus-12.
Sorenstam and Ochoa shared the lead entering the final round, but the Swede forged ahead with an eagle on the first. Ochoa birdied that hole, but found herself two back when Sorenstam birdied No. 2.
The women matched scores over the next eight holes with seven pars and one birdie, on the fourth. Ochoa got one stroke back with a birdie at the 11th. They both birdied 14, and Ochoa made it two straight as she also birdied 15 to tie Sorenstam in the lead.
Sorenstam, whose last win was at the U.S. Women's Open, regained the top spot with a birdie on 16. However, Ochoa's eagle at 17 got her to minus-20. Sorenstam joined her there as she birdied the par-5. The 35-year-old Sorenstam claimed the title with a birdie at the last.
'It was an incredible day. The finish was like a fairytale,' Sorenstam said. 'To come here at home, to play with Lorena in the last group head-to-head and in tough conditions, but to play like it was the best day ever, it doesn't get much better than that.'
Catriona Matthew and Laura Davies each carded rounds of 2-under 71 in the final round to share fifth place at 10-under-par 282. Bettina Hauert and Veronica Zorzi were one stroke further back.