Nordqvist, who played at nearby Arizona State, had a chance for a 60 in the LPGA Tour event, but her putt from behind the green at No. 18 barely trickled left of the hole.
Nordqvist is at 21-under-par 195, two shots better than Ariya Jutanugarn of Thailand and Stacy Lewis, who posted identical scores for the third straight day while being paired together. Each shot 67 in the third round.
So Yeon Ryu of South Korea is at 198 after a 64, one shot better than Angel Yin and In Gee Chun of South Korean. Yin carded a third-round 65 and Chun a 66.
World No. 1 Lydia Ko of New Zealand jumped into contention by firing a 63 that included six straight birdies to finish the round. She is at 200 for the tournament.
Nelly Korda shot 64 and also is at 200, three shots better than sister Jessica.
Michelle Wie, who was one shot off the lead after two rounds, shot a par 72 and dropped off the leaderboard.