The round was the lowest of Diaz’s four-year professional career.
Her 8-under 134 total was two strokes better than rookies Beth Bauer and Jeanne-Marie Busuttil and veteran Kris Tschetter.
Tschetter, winless in the last decade on the LPGA Tour, tied for fifth at the Farr last year, her best finish since undergoing hip surgery in 2000.
Fil-Am Dorothy Delasin, tied for second after a first-round 68, shot a one-over-par 72 and dropped into a share of 15th place while Jennifer Rosales, born and raised in the Philippines but now based in California, bounced back with a 70 after an opening 73.
Rosales, who won $78,000 for her strong seventh place finish in last week’s US Women’s Open, moved into a share of 49th place at 143 along with Sweden’s Charlotta Sorenstam (69-74) and Great Britain’s Catriona Matthew (72-71).
Delasin, nearing the $1 million mark in career earnings in the LPGA, had two birdies against three bogeys to join a big group of players six shots off the lead.
Starting her round on the 10th hole, Diaz was 1-under through six holes and 2-under for the tournament - making a 12-footer (3.6-meter) on No. 13 - before she turned things around with a three-hole blitz.
She hit an 8-iron to 15 feet (4.5 meters) at the par-4 16th, then hit a sand wedge to 3 feet (0.9 meters) and a sand wedge to 9 feet ( 2.7 meters) on the par-5 holes that close the back nine, each time rolling in the birdie putt.
She added three more birdies on the front side, including an 18-foot ( 5.4-meter) putt on No. 6 and a 12-footer on her final hole.
Her previous low on tour was a 65 in the third round of the State Farm Classic a year ago. She ended up fifth in that tournament.
Bauer had four birdies without a bogey in her 67.
Busuttil shot her second consecutive 68 despite a double-bogey on the first hole. She found a fairway bunker with her drive, blasted out into the rough, hit short of the green and chipped on before two-putting.
She wasn’t able to duplicate a miracle par she had in the opening round. She sliced her drive on the 10th hole out of bounds but ended up saving par when - after taking a penalty shot and hitting a second drive into the fairway - she holed a 9-iron from 142 yards.
Busuttil is traveling around the country on her honeymoon with her caddie and husband, Pete.
Tschetter’s 67, featuring four birdies without a bogey, followed the pattern set by Diaz. She made birdie putts that covered 14, 15, 20 and 30 feet.
Karrie Webb shot a 65 and Kelli Kuehne had a 66 to share fifth place at 5-under 137.
Defending champion Se Ri Pak - who has won the Farr three of the last four years - bounced back from a 72 with a 67 and led a group at 3-under 139.
Nancy Lopez, making her farewell trip around the LPGA Tour, holed an 8-iron from 134 yards on No. 6 for her 10th career ace. She shot a 70 and was right on the cut line at 2-over 144.