"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."
Pettersen posted 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 washed out. The 16-year-old Ko was trying to become the youngest ever major champion, but settled for a 70.
"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."
Top-ranked Inbee Park was looking 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.
Mika Miyazato of Japan held a one-shot lead going into the final round but collapsed completely with 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'll now 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."
American Lexi Thompson posted 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.
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, but clumsily 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 move level on the 12th, and Pettersen shook her head in disbelief as her second shot on hole 13 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."
Stacy Lewis won last month's British Open, but after a bright start the American finished six shots adrift of Pettersen in a tie for sixth along with countrywoman Angela Stanford and South Korea's Chella Choi.