Coming off an 11-stroke victory two weeks ago in Singapore in her season debut, Ochoa had six bogeys and two birdies on the hilly Bosque Real Country Club course. The 76 was her highest score since a 77 in the final round of the Ginn Open last April.
"It was not a very good day," Ochoa said. "I played really badly."
McGill, the 1993 U.S. Women's Amateur champion who is winless in 13 seasons on the LPGA Tour, eagled the 541-yard ninth hole
- her last hole - for a 5-under 67. She also had five birdies and two bogeys.
"I let it unfold and felt calm and comfortable and enjoyed myself out there today," McGill said. "I was not going to think about anything mechanical, just hit shots. I was tired of trying to be so perfect playing golf."
South Korea's Ji-Young Oh and Taiwan's Yani Tseng opened with 68s. Eva Dahllof shot a 69, and Pat Hurst, Gloria Park, Candie Kung and Eunjung Yi had 70s.
Meaghan Francella, a playoff winner last year over 2006 champion Annika Sorenstam, shot a 10-over 82. Playing alongside Ochoa, Francella had eight bogeys and a double bogey. Sorenstam is skipping the event, the first of three this year in Mexico.
Surrounded by well-wishers who cheered "Lo-re!" across the hilly course, Ochoa struggled off the tee and on the greens.
"I had some bad luck drives that left me in really bad spots, but the error was on the greens," Ochoa said. "I had really bad speed on the long putts."
The 18-time LPGA Tour winner has one victory in seven LPGA Tour starts in Mexico, the 2006 Corona Morelia Championship. She tied for sixth last year at Bosque Real, her best finish on the course.
"It's a punishing course," Ochoa said. "It's really key to have good first shots to put the ball on the fairway."