This is the first win for the 29-year-old Swede since the debacle at the 2016 US Women's Open in July.
Over the four days, Nordqvist posted 26 birdies, one eagle and just three bogeys to finish at 25-under 263, two shots better than Thailand's Ariya Jutanugarn, South Korean Chun In-Gee and Stacy Lewis of the US.
This is the first win for the 29-year-old Swede since the debacle at the 2016 US Women's Open in July where she was assessed a two stroke penalty in the playoff which allowed Brittany Lang to the claim the title.
"Of all the wins this is probably one of the ones that's going to be more special," she said.
Nordqvist's score to par came within two strokes of the LPGA record of 27-under set in 2001 by fellow Swede Annika Sorenstam and matched last year by Kim Sei-Young. All three rounds took place in Phoenix.
The win was the seventh on the USLPGA Tour and ninth internationally for Nordqvist, who played American college golf at nearby Arizona State.
"If it wouldn't be for me getting an opportunity to come to Arizona State University about ten years ago, I wouldn't be here today," said Nordqvist. "This truly still feels like home, even though I'm based in Florida.
"I have so many friends and family here. They feel like family, my US family. You know, couldn't think of a better place to be.
"I'm just so happy to be back. I wasn't even going to play a couple weeks ago and just ended up adding it at the last minute. Maybe it was meant to be."
Former US Women's Open winner Chun, reigning Women's British Open champion Ariya and 2011 ANA Inspiration winner Lewis all tried but failed to catch Nordqvist.
Chun rolled in six birdies in her bogey-free final round of 66.
Nordqvist's 25-foot birdie putt at 17 made for a ceremonial walk down the 18th fairway that even a bogey couldn't spoil.
World number one Lydia Ko, of New Zealand, shot 68 and finished 20-under in a bogey-free tournament.
Michelle Wie, in contention the first two days, shot final rounds of 72 and 70 and finished tied for 35th after she bogeyed her final two holes on Sunday.