It was the sixth LPGA Tour victory for Stanford and her first since 2012, when she won the HSBC Women's Champions in Singapore.
Lydia Ko of New Zealand totaled 67 and was four behind in a tie for 10th with Katherine Kirk (69) of Australia and Pepperdine, Brooke Henderson (68) of Canada, and South Koreans So Yeon Ryu (72) and Mi Hyang Lee (69).
Hall is one of three players tied in fourth place, along with South Korea's Inbee Park and American Angela Stanford. I haven't seen a lot of big misses or anything that you have to worry about. Her third, while struck solidly, forced a long and hard putt for par to win the tournament outright.
However, one of those came earlier this year when she played in the final group Sunday at the year's first major, the ANA Inspiration, and ultimately finished T9. "It was only my third year and I had no idea what I was doing, to be perfectly honest".
Olson is unlikely to have things all her own way, however, with several talented players in the chasing pack.
Stanford earned a $577,500 USA winner's check.
The 26-year-old signed for a 74 to slip into a four-way tie for second spot alongside fellow Americans Austin Ernst and Mo Martin and Sei Young Kim of South Korea.
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While this was only Olson's second legitimate chance at a major title, it was all too familiar territory for Stanford, who lost in an 18-hole playoff to Hilary Lunke at the 2003 U.S. Women's Open.
Tears flowed again as Stanford watched on a giant screen for Olson - who spent all day as outright or joint leader - to putt.
More than six years after getting the last of her five LPGA Tour titles, the 76th-ranked Stanford put her hands to her mouth in surprise before beginning an emotional round of television interviews.
Web.com - Sangmoon Bae won the Albertsons Boise Open to regain his PGA Tour card, birdieing the final hole for a one-stroke victory in the Web.com Tour Finals event. "It's forcing me to stay in the present and just hit one shot at a time".
That meant the 40-year-old from Fort Worth, who had feared the worst after dropping a shot behind Olson when she shot a double bogey at the 16th hole, collected the winner's cheque of $577,500 (£442,000/€496,000).
The English golfer got off to a sluggish start with a bogey on the par-4 2nd at The Dutch in Spijk, and reached the turn 1 under for the day before reeling off five birdies on the back nine to reach 13 under for the tournament.