The pair carded four-under 69s to sit two shots clear of a group of four players ??? China???s Xiyu Lin, South Korean Shin Ae Ahn and Thai duo Nontaya Srisawang and Pavarisa Yoktuan.
Morgan and Park made the most of the more favourable afternoon draw, playing under overcast skies in drizzly conditions after a wet and windy morning.??
Morgan, who is still awaiting her first Ladies European Tour victory, was pleased with her game after making five birdies and one bogey on the Blackstone Course.
She said: ???I had a really good finish and birdied the last three holes, but I played really steady and hit some really good hybrids into the longer par fours and missed a couple of putts early on so all in all I was pretty happy.
???I three-putted the par-three 15th and gave myself a talking to and birdied the last three.???
Five-time major champion Park was less impressed with her four birdies and two bogeys, despite an eagle on the par-five 18th.
She said: ???I didn???t have as many opportunities as I would have liked as the iron shots were a bit off today and I only eagled one par five and had par on the others.
???The key to this golf course is making birdies on the par fives so if I can do that tomorrow I think it will be a great round.???
Park???s main rival, Norwegian world No 5 Suzann Pettersen, who won the 2013 event and finished second in 2014, opened with a level par 73 to share 14th place.
The World Ladies Championship is unique in golf in that three titles are contested simultaneously in one event, with an individual professional stroke play, amateur and professional team aggregate prize, for the leading pair representing their country.
In the team competition, South Korean pair Park and So Yeon Ryu set the pace with their combined score of five under par to lead by three over the China A team of Xiyu Lin and Weiyao Lu and Thai pair Srisawang and Yoktuan.
In a share of seventh place on one under par, China???s Lei Ye holds a two stroke lead in the amateur race over compatriot Xiang Sui.??