Annika Sorenstam, who is seeking her fifth consecutive victory on the LPGA Tour, posted a 2-under-par 70 to share fourth place with Carin Koch, Juli Inkster and amateurs Michelle Wie and Morgan Pressel.
Jones, a 13-time winner on the LPGA Tour who has never captured a major championship, played a sandwedge inside 5 feet for a birdie at the par-5 second. She coasted around the turn with a string of pars as the wind picked up before her approach to the par-4 15th landed within 15 feet of the cup.
'Fortunately I didn't make any bogeys today, but it's the type of golf course you know that you're going to make them, so you want to take advantage of every birdie that you can,' said Jones. 'I felt that I had to be really patient having missed a few opportunities. Last thing you want to do is get a little bit frustrated.'
Jones has come close several times in her hunt for a major title, including a couple of top-3 finishes on the Dinah Shore Course at Mission Hills Country Club. She has stated that she will retire at the end of this season, and the time is running out for her to taste major glory.
'I'm trying to have fun,' said Jones. 'I'm trying to enjoy every tournament that I go to because I know this is probably going to be the last. Except for here, I may come back, I may come back to play a couple majors or something like that, but I don't really want to take on the magnitude of what you have to do every year.'
Stupples ran off a pair of birdies and a bogey over her first nine holes. She picked up a birdie at the par-5 11th and moved to 3 under with a birdie at the par-4 13th. Stupples found trouble with a bogey at the 14th, however, but rolled in a 14-foot putt for a birdie at the par-4 16th to grab her share of the lead.
'I enjoy the majors,' said Stupples, who won last year's Women's British Open. 'I like them for the challenge the courses bring. I know that you have to fight for every single shot out there, so it helps me concentrate a little better.'
Kim bogeyed the first but recovered with a birdie at the par-4 third. She then birdied the par-5 ninth and added a birdie at the par-5 11th.
The Korean tallied another birdie at the par-4 15th for her piece of first.
Sorenstam has won her last four starts on the LPGA Tour dating back to the end of the 2004 season. She knocked off Lorena Ochoa in a playoff last week at the Safeway International and looked to carry her momentum into the season's first major with an eagle at the par-5 second.
The Swede then birdied the fourth but gave a shot back with a bogey at the par-3 eighth. Sorenstam dropped another shot at the par-4 12th after she missed the green with her approach but she responded with back-to-back birdies from the 13th to climb to 3 under.
Sorenstam was unable to find the green at the par-3 17th and chipped her second shot 8 feet from the hole. She was unable to convert en route to another bogey to finish one shot behind the leaders.
'Not a bad start,' said Sorenstam, who won this event in 2001 and 2002. 'You cannot take anything for granted around here. I had some good holes and had some bogeys and couldn't really rebound with too many birdies.'
Wie dazzled the crowds early on with a birdie at the second. She then hit her third shot to 4 feet for a birdie at the par-5 ninth and converted a 5-foot putt for a birdie at the par-4 10th to make it two in a row.
The 15-year-old, who has a pair of top-10 finishes at this event, parred her next six holes but missed the green at the par-3 17th. Wie chipped to 6 feet but was unable to save par.
'I just have to again move that one step ahead,' Wie said of challenging on the LPGA Tour. 'I think that I'm getting there. I just have to work on it a little bit harder.'
Jennifer Rosales, Liselotte Neumann, Sophie Gustafson, Lorie Kane, Pat Hurst, Donna Andrews, Dorothy Delasin, Sherri Steinhauer and Michelle Estill share ninth place at 1-under-par 71.
Defending champion Grace Park, who is suffering from a bad back, collected a birdie and two bogeys to finish four shots off the lead in a group at one- over-par 73.