Overnight leader Natalie Gulbis struggled to a round of 75 at Tres Marias Residential Golf Club to fall back into a tie for third place with Maria Hjorth at 3-under-par 141.
Koch opened her round with a bang when she holed out from 97 yards for an eagle at the par-4 first.
'I hit it really well and it was headed at the hole,' said Koch. 'It hit once and bounced and went right in the hole. That was a great way to start.'
Koch kept on rolling with a birdie at the par-5 fifth after she played her third shot to 8 feet. She missed a 6-foot par putt at the sixth but answered at the par-5 eighth and hit a wedge to 3 feet for a birdie.
The 33-year-old moved to 8 under with a birdie at the par-5 16th but three-putted the closing hole for a late bogey.
'I definitely left some putts out there today,' said Koch. 'I had so many chances. I think a lot of players are leaving a lot of putts out there because the greens are very difficult to read. I am happy with my round but a little frustrated that I did leave some out there.'
Ward, who won the LPGA Takefuji Classic last week, jumped out of the gate with a birdie at the first but she tripped to a bogey at the third and found trouble again with a bogey at the seventh. Ward's problems continued at the 10th when she missed the green with her approach en route to another bogey but she got one back with a birdie at the par-4 12th.
Ward then birdied the par-3 13th and hit her second shot to 3 feet for a birdie at the 15th. She followed with a birdie at the par-5 16th and made it three straight with a birdie at the par-4 17th after her approach shot landed 9 feet from the cup.
'I feel good about my game,' said Ward, who posted a 69. 'I don't feel any different about it than last week, so that is a positive.'
Sung Ah Yim, Leta Lindley, Giulia Sergas, Audra Burks and Charlotta Sorenstam share fifth place at 1-under-par 143.
Lorena Ochoa shot a 71 to finish one shot further back at even-par 144. She was joined by Jill McGill, Stacy Prammanasudh, Kelli Kuehne, Yu Ping Lin, Kris Tschetter, Dawn Coe-Jones and Catriona Matthew in a tie for 10th.
The cut fell at eight-over-par 152 with 78 players qualifying for the final two rounds.