Yi, 21, made a fairway shot for an eagle at No. 10 and collected eight birdies without a bogey to post her best score on the LPGA Tour by five shots.
Yi moved to 18-under 195, four shots better than Song-Hee Kim (64) of Korea and Morgan Pressel (67) going into Sunday's final round.
Mikaela Parmlid (62) was in a group of seven players two strokes further back at 12-under 201.
Yi's 61 was not a course record. Defending champion Paula Creamer, who withdrew Thursday, had a 60 in the first round last year. Annika Sorenstam has the only 59 in LPGA Tour history.