The 31-year-old Swede, ranked 95th in the world, beat seven-time major winner Inbee Park in an absorbing eight-hole sudden-death playoff which finished Monday.
The pair had tied with American Jennifer Song at 15 under to take the event to a playoff for the second straight year after So Yeon Rhu beat Lexi Thompson last year.
Song exited at the third extra hole, but after floodlights were used to illuminate the green for a fourth hole, darkness prevailed to set the stage for a Monday shootout at Mission Hills, California.
And after three tight holes, Lindberg eventually holed a putt from 25 foot for birdie on the 10th green to beat the 29-year-old Olympic champion from South Korea.
Lindberg's previous best major finish and only top 10 in 31 events was a tie for fifth in the 2015 US Open.
Along with caddy and fiance Daniel Taylor, Lindberg held hands with her mum and dad and performed the ceremonial winner's dive into Poppy's Pond.
"It's just bigger than I could ever dream of," Lindberg told a media conference.
"The only reason that I play golf is because of my parents. They're the ones who introduced me to the game, and I'm so happy they can be here and share this moment with me.
"Then to be able to share it with Daniel on and off the golf course, it just makes it so special.
"We're going to have so many good memories to share for the rest of our lives. Hopefully tell our future family about."
Lindberg led after an opening 65 and was still tied at the top with South Korea's Sung Hyun Park at halfway before taking a three-shot cushion into the final round.
But her closing 71 allowed Park and Song to catch her with rounds of 67, setting up the showdown.
The Swede came within centimeters of potentially clinching the title on Monday's first hole, leaving a 30-foot birdie putt agonizingly short on the 10th.
It left Park with a 20-foot putt to win, but she missed and gave herself a few heart-stopping moments before holing the tricky four footer coming back.
On the par-three 17th, it was Lindberg's turn to sweat as Park holed from 15 feet for par after driving into the left bunker.
However, the Swede chipped up to 12 feet from the front rough and holed her putt to take the playoff back to the par-five 18th.
Park laid up in front of the water guarding the green with her second and missed her birdie putt, gifting Lindberg a six-footer for the title.
However, she missed and the pair moved back to the 10th.
This time, Lindberg holed her long putt and watched as Park failed to match her from 10 feet.
"The putt Pernilla made on the last was a champion's putt. You really can't beat that.," said Park. "I'm really happy for her."
Lindberg becomes Sweden's sixth major champion alongside Anna Nordqvist, 10-time champion Annika Sorenstam, Helen Alfredsson, Liselotte Neumann and Jenny Lidback, who was born in Peru to Swedish parents.
All of those were also winning their first LPGA tournament at the same time.