Inkster, 49, would be the oldest golfer to win an LPGA event if she can pick up career title No. 32 on Sunday while Miyazato, 24, will be shooting for her second tour title in as many weeks. They are at 7-under 209 after 54 holes.
Momoko Ueda, who tied for Saturday's best round with a 68, is among four players tied for third two strokes behind the leaders. She, Park Hee-young (69 Saturday), Sun Young Yoo (71) and Han Hee-won (71) have three-round totals of 5-under 211.
Second-round co-leaders Kim Song-hee and Angela Stanford were both over par Saturday. Stanford shot 2-over 74 and is tied for 10th, four strokes off the lead. Kim turned in a 3-over 75 and is tied for 15th another stroke back.
Miyazato had three birdies and two bogeys on the front side Saturday and grabbed a share of the lead with an eagle at the 269-yard, par-4 16th hole by dropping a 30-foot putt.
Inkster had four birdies and a bogey with two of the birdies coming on par 3s.
Swim Week Miami Beach 2014 [PHOTOS]