She also shot a 68, for a total of 142.
Barber shot 68 for a 54-hole total of 208, two shots better than the leading pace in the Tour division.
She shot a 71 today with birdies on her last two holes for a two-day total of 145.
And in today's second round of the Open he shot 71 for a 36-hole total of 138, six under par.
Joyce, who was one stroke off the lead after Friday's 68, shot 73 for a two-round total of 141.
Price shot a par 72 for a 54-hole total of 210.
Couples shot his second consecutive four-under-par 68 for a 72-hole total of 15-under 269.
Greg Norman shot 72 for a total of six over par 150 to miss the 36-hole cut by two shots.
And if he had shot 65 for a total of 280, he would have won by a stroke.
King shot a 71 today for a total of one-under 143.