Sorenstam carded a 2-under 70 in the final round to complete the event tied with Lorena Ochoa at 11-under-par 277. Ochoa struggled to a 2-over 74 on Sunday.
Juli Inkster (72) and Soo-Yun Kang (76) shared third place at 8-under-par 280. Liselotte Neumann, the 1998 champion of this event, posted a 1-under 71 to close the tournament at 7-under-par 281. She shared fifth place with Rosie Jones, who was the 1998 runner-up.
Sorenstam two-putted for birdie from 22 feet out on the 72nd hole to get to 11-under. Ochoa had a 12-foot birdie try at the last to win, but it slid by the right edge.
Ochoa teed off first in the playoff on the par-5 18th. She pulled her tee shot into the water left of the fairway. Sorenstam played her tee ball without issue on the Prospector Course at Superstition Mountain Golf and Country Club.
Ochoa took her drop, then knocked her third into the right rough. The Mexican hit her fourth shot over the green and missed her par chip.
Sorenstam, meanwhile, knocked a fairway-wood up near the green. She pitched her third shot to 7 feet and two-putted for par and her 58th win on the LPGA Tour. That ties her for fourth on the LPGA's all-time wins list with Louise Suggs.
'I've learned the lesson the hard way not to ever give up, but it wasn't really looking good,' said Sorenstam, who pocketed $210,000 for the win. 'I saw Lorena climbing up the leaderboard with more and more birdies, and I was trying really hard, but I just couldn't make any birdies.
'And it wasn't until the 16th when I heard that she double-bogeyed, and when I was on 18, I realized there's a big chance here.'
Sorenstam began her day four strokes behind Ochoa, who held at least a share of the lead after each of the first three rounds. The Swede opened with five straight pars before stumbling to a bogey at the sixth.
The Swede came right back with a birdie on the seventh. Around the turn, Sorenstam moved to 10 under with a birdie at the 11th. She remained there with six consecutive pars before her two-putt birdie at the last.
'The 4-wood I hit is probably one of the better shots I've hit in a long, long time,' Sorenstam said. 'I was so pumped to come up there and have a great opportunity to win. You know you're not always going to win, but when you do, it just makes it so much sweeter.'
Ochoa led Kang by one stroke entering the round, but was four strokes clear of Sorenstam, who began the round alone in third place. The Mexican struggled to bogies at the third, fifth and sixth to slide back to minus-10.
Ochoa fought back to even par for her round as she birdied Nos. 7, 8 and 10. She looked to be in control when she sank a 12-foot birdie putt at the 15th to again move four shots clear of Sorenstam.
The 23-year-old Ochoa found a fairway bunker off the tee at 16. After a poor second shot, she knocked her third on the green 15 feet from the hole.
However, she faltered to a three-putt, double bogey. Her troubles continued as she bogeyed the next after missing the green to the left.
Playing one group behind Sorenstam, Ochoa watched as Sorenstam birdied the last to tie the two at minus-11. Ochoa could only par the last forcing extra holes.
'It was a really hard day for me,' Ochoa admitted. 'I didn't feel comfortable since the morning. I was out of my rhythm and I was anxious out there and swinging to quick. So, I gave the tournament away. Annika beat me.
'She gave me a good chance to win the tournament, and I just made really big mistakes at the end. I'm pretty upset, but I'm going to try not to be too hard on myself. I'm going to learn from this.'
Michele Redman fired a 5-under 67 to finish the tournament alone in seventh place at 6-under-par 282. Laura Diaz (69), Candie Kung (72), Gloria Park (72) and Natalie Gulbis (68) finished one shot further back at minus-5.
Amateur sensation Michelle Wie closed with a 1-under 71. She shared 12th place at 4-under-par 284 with Siew-Ai Lim and SBS Open winner Jenny Rosales.
Grace Park, the defending champion at next week's Kraft Nabisco Championship, the first major of the season, withdrew prior to the final round with a sore back. She is expected to be ready to defend her title at the Nabisco though.