Pettersen, the leader after the second and third rounds at Ko Olina, bogeyed the final hole of regulation to set up the playoff on the par-4 18th. The 32-year-old Norwegian closed with a 5-under 67, and Salas had a tournament-record 62 to finish at 19-under 269.
"I thought 20 was going to do it," Pettersen said. "That would take a fantastic round from anyone behind me, and it would take some good golf from me, but that was kind of the number I was shooting for."
Salas had a double-bogey on the playoff hole. She played a nine-hole stretch in 9 under, birdieing Nos. 8-9, holing out from the fairway for eagle on the par-4 10th and adding birdies on Nos. 12-16.
"Chunk is not bad, but if you have water it's really bad," Salas said. "But I still had a chance, and that putt didn't go in. Not everything is going to fall, but I played my butt off today."
The 23-year-old American was coming off a devastating collapse two weeks ago in the Kraft Nabisco Championship when she closed with a 79 to tie for 25th after beginning the final round three strokes behind playing partner and eventual winner Inbee Park.
"From shooting a 79 at Kraft to shooting a 62 here in Hawaii, like that just -- I can't really describe the feeling, just I feel so proud of myself to put that 79 in the back of my mind and just to go out and play some golf," Salas said. "I took a big risk in using the short putter, but I felt extremely comfortable. I felt like me again."
Pettersen won her 11th LPGA Tour title. She had consecutive LPGA Tour victories late last season in South Korea and Taiwan and won a Ladies European Tour event last month in China.
"My game has been feeling great," Pettersen said. "It's nice that I have kept kind of the progress that I had from Kraft."
Pettersen birdied the par-3 12th get to 18 under, three strokes ahead of Salas, then bogeyed the par-5 13th after she lost her ball on her drive when she was distracted by a car honk. She birdied Nos. 14, 15 and 17 to reach 20 under, but couldn't get up and down for par on 18.
"I've kind of figured out how I play well, and I play well when I stay aggressive," Pettersen said. "I hate to play defensive and I hate to play away from the pins, and obviously at times you have to. That's when the experience comes in. But for me to shy away and not step on the pedal, that's not me. If I make an error being too aggressive, I can live with it. But if I make an error playing defensive trying to protect something, I mean, I wouldn't shoot myself, but it's hard for me to accept it."
Salas has four top-10 finishes in seven starts this year.
The daughter of Mexican immigrants, she was introduced to the game when her father, the head mechanic at Azusa Greens Golf Course west of Los Angeles, did some handyman jobs for the club pro and, instead of pay, asked him to teach his daughter to play. She went on to star at the University of Southern California, where she was a four-time All-America selection and helped the Trojans win the 2008 NCAA title.
"My mom is here, everyone has been pulling for me, and I just -- baby steps," Salas said. "I've got to just keep working on the things I'm working on, and the good thing is I'm going home tonight to see my family tomorrow for a day, and I'm sure they're very proud of me."
Pettersen looked up at the leaderboard and was surprised to see Salas' name up there.
"I birdied 15, and then I think I was aware that she was like 18 under," Pettersen said. "So I mean, she wasn't going anywhere, and I'm like, 'Oh, my God, where did she start this day? Because I didn't remember seeing her next to my name on the list yesterday.
"She's a tough cookie. She's been playing fantastic. She's just got to keep putting herself in this position, and she'll get her win."
Ariya Jutanugarn, the 17-year-old from Thailand, shot a 66 to finish third at 15 under.
The top-ranked Park had a 67 to tie for fourth with I.K. Kim at 13 under. Kim shot 65.
"We played one week and I'm still No. 1, so I know I kind of deserve No. 1 spot now," Park said. "I played very good golf this week. The first two rounds my putts didn't really fall, but round three and four it was much better. Very happy with my game at the moment and very confident."
Lydia Ko, the 15-year-old New Zealand amateur who won the Canadian Open in August to become the youngest LPGA Tour winner, tied for ninth at 10 under after a 6. The South Korea-born Ko has two other pro victories, the New South Wales Open last year and New Zealand Women's Open this year, and won the U.S. Women's Amateur last season.
Second-ranked Stacy Lewis also finished at 10 under after a 71.
Local favorite Michelle Wie shot a 68, her best round of the tournament, to finish at 5 under. She broke 70 for second straight day and for only the third time in 22 rounds this season.