Pettersen calmly rolled in a putt for par to seal the victory, then leaned back and held her head in her hands, hugged her caddy and laughed as she was sprayed with Champagne.
"I might start to get a bit emotional," Pettersen said, her voice wavering, as she collected the trophy.
It was her first major since the LPGA Championship in 2007.
Pettersen shot a 3-under 68 to finish with a 10-under total of 203 after the tournament was reduced to three rounds when Thursday's play was rained out. The 16-year-old Ko, who was trying to become the youngest major champion, finished with a 70.
American Lexi Thompson shot a 68 to finish four shots back in third place, with South Koreans So Yeon Ryu and Se Ri Pak five shots behind in a tie for fourth.
Top-ranked Inbee Park aimed to become the first golfer to win four majors in a year, but finished way out of contention. This was the first year that Evian counted as the fifth and final major of the year on the women's calendar.
It marked Pettersen's second successive tournament victory after the Safeway Classic this month.
"I don't know if it's quite sunk in yet that I've won another major. It's been a while but I'm pretty lucky to say that I've won two," Pettersen said. "Hopefully this is just the start. It's been such a great month, five weeks for me, starting off with the Solheim (Cup). It was a great kick-start for what became the best month of my career."
The third-ranked Pettersen plans to have "one heck of a party" to celebrate, before focusing on her goal to earn the No. 1 ranking.
"This is part of the process, you have to win tournaments, you have to win majors," said Pettersen, who in the past has been hampered by a fiery temperament. "I've had my hurdles over the years."
Mika Miyazato of Japan held a one-shot lead going into the final round but struggled to a 79 that left her in a tie for 19th.
That left Ko -- at 16 years, 4 months, 22 days -- as Pettersen's main challenger. But the New Zealander bogeyed the 13th to fall two shots behind and never looked likely to make a comeback. Her chip for birdie at the 18th -- which would have put some pressure on Pettersen -- stopped just left of the hole.
"She's such a great competitor. She keeps us on our toes," Pettersen said. "She's 16 and she's good enough to win tournaments, to win major championships. She's a future star for this game."
Ko will have to wait until next year for a chance to break American Morgan Pressel's record of youngest major winner. Pressel was 18 years, 10 months, 9 days when she won the Kraft Nabisco Championship in 2007.
"I don't think I felt that nervous today, but coming down the last two holes I thought Suzann had it in the bag," Ko said. "It was really good to know that I could come close to a winner at a major. Hopefully, next year it will be a 72-hole event."
An overnight downpour rendered the course soggy and led to a 90-minute delay in the morning.
"I thought today we would fight the weather more than we did, so it was a walk in the park just to stay dry," Pettersen said. "I didn't know what to expect with the weather we had overnight. But the greens were good."
When play got started, Ko opened her round with a birdie while Pettersen had birdies on the second and third holes. Pettersen bogeyed the seventh when she over-hit her approach shot.
She recovered with a birdie on the next hole and led Ko by one shot and Ryu by two after the front nine.
Ko looked stern-faced after missing a chance to tie it on the 12th, and Pettersen shook her head in disbelief as her second shot on the 13th drifted wide into the choppy rough. But she ended up saving a tricky par while Ko had to settle for bogey, leaving her two shots ahead.
Ko looked downbeat when she missed another birdie chance on 17.
"I didn't feel confident with my putting today. I left a couple short," Ko said. "I misread some putts. I won't blame the greens that were bumpy, and blah, blah, blah. I don't blame others."