The German, who held a two-stroke lead overnight, had a 71 to see her advantage cut in half, with Spain's Carlota Ciganda a shot behind.
"After the last few holes, I'm pretty happy it's over now," said Masson. "I don't know what went wrong really. It was just a few bad shots, but it's good that it's over and then I can just relax now and tomorrow I'll be fine again."
Ciganda had a 70 to stay close to Masson, while world number one Inbee Park (70), 18-year-old Moriya Jutanugarn (66) and Kathleen Ekey (67) were two shots back.
Jutanugarn had the day's best round, a bogey-free 66.
Stacy Lewis, who can regain the world number one slot in she finished in the top five in Texas, shot a par 70 to end the second round tied for 36th.
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- Carlota Ciganda