Saigo, a joint overnight leader and last season's rookie of the year, birdied the par-5 18th in regulation for a two-over 74, leaving her tied with South Korean Hyo Joo Kim, China's Ruoning Yin, Thai Ariya Jutanugarn and American Lindy Duncan.
They were tied at seven-under 281 at The Club at Carlton Woods in Texas, setting up the largest play-off at an LPGA major in history.
Saigo won the the next time up the 18th after Yin and Jutanugarn had birdie tries lip out.
Jutanugarn had bogeyed the 18th in regulation after stubbing her third short only inches, having led for most of the day.
The former world No.1 needed par at the last hole to win outright but, in a bizarre sequence on her third stroke, she missed nearly her entire ball, which moved very slightly forward.
The five players returned to the 18th tee. Yin was the only player to hit the green in two shots, but she badly misread the mid-range eagle putt and also lipped out her birdie try.
While Duncan ended up with a bogey, Kim and Jutanugarn also missed their birdies.
That left Saigo, who went over the green on her second shot and pitched it to about five feet for the winning birdie.
Saigo, 23, had not won on American soil before Sunday. Ranked 37th in the world, her six career victories all came on the LPGA of Japan Tour.
The victory comes after runner-up finishes at the CPKC Women's Open and Buick LPGA Shanghai last year.
"Last year it was a very intense competition," she said.
"I was so close but I was not able to make it. It was very disappointing. This year I was able to win and earn the LPGA title and I'm extremely excited about this."
It was another week of what might have been for Australia's two-time major champion Minjee Lee.
She started the day five shots from the lead but could only manage a 74, with four bogeys, as she tied for 14th, five strokes outside the play-off.
Lee has three top-10 finishes from eight starts this year and has repeatedly been in the mix going into the weekend only to falter.
Of the other Aussies, Steph Kyriacou shot a 72 and climbed to tied 30th at two over and fellow Sydneysider Cassie Porter (73) finished equal 40th at plus three on her major championship debut.
Gabriela Ruffels was a further shot back in joint 44th after closing with a 76.
With AAP
