Jiyai's fifth birdie in the final round took her one stroke clear of overnight leader Pressel, whose putt to force a playoff then rolled agonizingly over the hole without dropping in.
The 22-year-old Jiyai is the first South Korean to win the Evian Masters and takes home prize money of $487,500. She now has seven LPGA Tour victories in two years, winning her first at the British Open in 2008.
Jiyai briefly held the No. 1 world ranking for seven weeks after Lorena Ochoa's retirement earlier this season.
Pressel (70), who started the final round two strokes clear, walked over and hugged Jiyai after missing her putt.
Pressel's downhill putt from the right of the green gathered speed, and she sank to her knees when it rolled over the hole _ giving her a share of second with Na Yeon of South Korea (66) and the 15-year-old Thompson from the United States (67).
"It was close. It looked like it was going in and it just sneaked out," Pressel said. "I hit a lot of good putts on the back nine. I had one birdie and all I tried to do was hit aggressive putts and not leave them short."
Suzann Pettersen of Norway (66) was fifth at 12 under. Defending champion Ai Miyazato (68) finished tied for 19th at 5 under. American pair Michelle Wie (71) and Criste Kerr (72) were tied for 31st at 2 under.