Sorenstam blew a four-shot lead in regulation. She starting with a double bogey on the first hole and had bogeys on the last two, finishing at 4-over-par 76.
Teske carded a 71, tying Sorenstam at 8-under 280.
Both players parred on the first playoff hole, Teske after blasting out of a fairway bunker and into another bunker behind the green. She hit a wedge to within 4 feet and saved par.
On the next, Teske's approach shot landed 6 feet from the cup, and she holed it after Sorenstam's first putt from about 13 feet stopped short.
Teske, 3-1 in playoffs, improved to 2-1 in head-to-heads with Sorenstam. She beat the Swedish star in the 1999 Betsy King Classic and lost to her at the 2000 Jamie Farr Classic.
It was Teske's fifth career victory and second in two seasons. She won the Evian Masters in France last year.
Sorenstam, who played 20 holes without a hint of her trademark burst of birdies, was going after her third win in as many starts and was on a course where she shot the first 59 in a women's tournament during the second round at Phoenix in 2001.
The low round and her 27-under 261 total are two of the six LPGA records Sorenstam set or tied.
This year was different as all the players struggled in chilly conditions for three days and didn't seem able to improve on Sunday when there was less wind and warmer temperatures. The final 8-under was the highest winning score at Moon Valley Country Club since Laura Davies won at 8-under in 1996.
Mi Hyun Kim (72), Cristie Kerr (75) and Akiko Fukushima (75) tied for third at 284, with Jeong Jang (68) and Juli Inskter (71) at 285.
Sorenstam beat Karrie Webb in a playoff to win the unofficial-money Australian Masters last month, and overcame Lorie Kane in a playoff to win the season-opening Takefuji Classic in Hawaii on March 2.
This time, she seemed set to win in regulation when she took a three-shot lead into No. 17.
But there was a two-shot swing on No. 17, where Teske made a 15-foot birdie putt and Sorenstam bogeyed after three-putting from 25 feet.
On the 18th, Teske nearly holed a 50-foot putt for birdie. The ball hit the back of the hole and rolled away, leaving a 4-footer for par that the Aussie buried.
Sorenstam's second shot at No. 18 skipped over the firm green and landed in a back bunker, drawing a gasp from the gallery. She got the ball out, but it ran 7 feet past the hole. She two-putted for her third bogey of the round.
Sorenstam, who has won 14 of her 32 career titles since 1999, had what amounted to a meltdown when she double-bogeyed the first hole, a 349-yard par-4 which demands the kind of accurate drive that she usually hits.
This time, she drove into trouble on the right, punched back out to the fairway, hit her approach shot into a greenside bunker and two-putted after blasting within 3 feet of the flagstick out of the sand.
At the time, it seemed like just a blip.
But Sorenstam finished with 33 putts in regulation, and Teske offset bogeys at Nos. 2, 9 and 15 with four birdes.
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