The Swedes ended at 7-under-par 281, while Scotland's duo took second place at 4-under-par 284.
Scotland's Janice Moodie posted an even-par 72, while her partner, Catriona Matthew, fired a 3-under 69. Their three-under total of 141 was the lone team score in red figures on the day. Becky Brewerton and Becky Morgan of Wales stumbled to a 4-over 148 to end in third place at even-par 288.
The United States pair of Paula Creamer and Natalie Gulbis, only managed a 2-over 146 to take fourth at plus-1.
Korea's Meena Lee and Bo Bae Song, who played alongside the Swedes, struggled badly as they posted a 9-over 153. They fell into fifth place at 2-over-par 290. The Colombian sister team of Christina and Marisa Baena were one stroke further back at plus-3 at Gary Player Country Club.
Sunday's action saw the teams playing singles competition with each player's score counting towards the team total. Friday's play was better ball, with only the team's best score counting, while Saturday saw the field play the foursomes, or alternate shot, format.
The Swedes were never seriously challenged on Sunday. Sorenstam birdied the second to move them to minus-11, but Neumann's bogey on the third gave that stroke back.
Neumann stumbled to another bogey at the seventh and Sorenstam dropped her first stroke at the next as the team's score fell to minus-8. However, they each birdied the par-5 ninth to make the turn at 10 under, which was good for a seven-shot lead at the time.
Trouble loomed on the back nine as both bogeyed the par-4 11th. Neumann bogeyed each of the following two holes as well, as they tumbled back to 6 under.
Korea and Scotland were closest at the time, but both faltered. Lee double- bogeyed the 14th and Korea fell off the pace. The Scots dropped three strokes in a four-hole stretch to fade away.
Sorenstam, the top player in the women's game, steadied the ship for the Swedes with an eagle at the par-5 14th. Sorenstam would go on to par her final four holes, while Neumann gave one last shot back at the 17th before she closed out the round with a par.
'The eagle on 14 was crucial,' Sorenstam said. 'We struggled a bit on the back nine and the momentum certainly swung our way again with that eagle.'
'I was struggling there with my bogeys at 11, 12 and 13 and it was really important when Annika eagled 14,' said Neumann. 'That gave us some breathing room again.'
South Africa's pair posted a 2-over 146 to share seventh place with Finland at 4-over-par 292. Germany and Australia were two strokes further back at plus-6.
Japan, which won the crown in 2005, finished at 8-over-par 296 and alone in 12th place.