World number nine Thompson, 22, carded six birdies in the ANA Inspiration at Mission Hills, California to lead Norway's Suzann Pettersen (68).
England's Charley Hull, 21, had three birdies in a one-under 71 as she slipped eight shots off the lead.
She is tied for 11th on five under par with world number one Lydia Ko.
The 19-year-old from New Zealand, who won this tournament last year to collect her second major title, bogeyed the first hole but posted two birdies and 15 pars for a one-under 71.
Seven-time major winner Inbee Park is in a group of four on 10 under that includes fellow South Korean So Yeon Ryu, the 2011 US Women's Open champion.
The event is back on schedule after delays caused by stormy weather but Thompson was among 56 players who had to complete their second rounds on Saturday before playing the third.
The halfway leader, who won the 2014 title, said: "Experience always helps me out, but I'm just going to focus on one shot at a time, relax out there between shots and just focus on doing my routine."
Pettersen, winner of the Women's PGA Championship in 2007 and the 2013 Evian Championship, has been runner-up in the event on three occasions and said: "I'm driving the ball well and that's a major key on this golf course. If you do, you can kind of attack it as well.
"The leaderboard is packed behind me. You've got to expect to go out there and shoot low. There's a lot at stake, but I'm all in for it."
After two sub-70 rounds, former US Women's Open champion Michelle Wie returned a 71 and shares seventh on eight under.
England's Mel Reid, the only other Briton to make the cut, is two over par after a mixed round of five birdies, five bogeys and a double bogey saw her post a two-over 74.
American Lexi Thompson takes a two-shot lead into the final round of the first women's major of the season after a five-under 67 took her to 13 under.