She finished on a four-under 69 and was joined by World No.2 Inbee Park on top of the leaderboard.
They share a two-shot cushion with over China's number two-ranked golfer Xiyu Lin, who had set the early pace.
England's Trish Johnson is three shots off the lead after an opening 72.
Morgan was two-under after the first nine with birdies at the short fifth and the par-four ninth, but dropped a shot at the 15th.
She bounced back with a run of birdies on the back nine for a share of the lead.