The 18-year-old Thompson shot a 5-under 67 in rainy conditions to reach 13-under 203 at Guadalajara Country Club. She had a one-stroke lead over South Korea's I.K. Kim.
''The rain definitely affected us somewhat, but I teed off a little bit later with the delay,'' Thompson said. ''I think just controlling my yardages out here is pretty big and playing consistently. My irons were a lot closer today, and I dropped a few longer putts.''
Thompson won the 2011 LPGA Navistar Classic at 16, and took the LPGA Malaysia last month for her second tour title. She protected third-round leads in both victories.
''It gives me confidence going into tomorrow, but I know there's a lot of great players right behind me, and I know I have to play well,'' Thompson said. ''I know I have to shoot another 4 or 5 under tomorrow. I'm just going to go out with the same attitude and just commit to every shot.''
Kim birdied the final two holes for a 67.
''Winning is amazing, but just being able to play golf and just have fun, that's the first thing,'' Kim said. ''If I can win twice, I mean, why not, I think it would be really great.''
She had only 22 putts in the round.
''At the start of the day it was pouring down, so we didn't expect the rain, but everybody was in the rain,'' Kim said. I had a good start, I made birdie on 1 and 2, and I think that kind of helped going forward. Basically, I really like this golf course. I have a good feeling for the course, and I've been practicing. It's just nice to see the result.''
Third-ranked Stacy Lewis was third at 11 under after a 67.
Ryu was another stroke back after a 71. Nordqvist and Phatlum each shot 72 to remain 9 under.