Wendy Ward, who shared the 54-hole lead with Koch, posted a 78 to fall back into a tie for third with Catriona Matthew at 2-under-par 286. First-round leader Natalie Gulbis was one shot further back at 1-under-par 287 along with Dorothy Delasin and Soo Young Moon.
Koch made an early move with a birdie at the par-3 third, but she found trouble with a bogey at the following hole. Ward then moved ahead with a birdie at the fifth, but Koch matched her at 9 under with a birdie at the par-3 sixth.
'I was trying to feel comfortable, calm and play my game,' said Koch. 'I tried not to pay too much attention to what anyone else was doing.'
The Swede took the outright lead with a birdie at the seventh and Ward fell two shots off the pace with a bogey at the eighth. Koch then stumbled on the back side with back-to-back bogeys from the 10th to again forge a tie.
Ward's round began to come apart with a double bogey at the par-4 12th and Koch took advantage with a birdie at the par-4 15th. Ward then triple bogeyed the par-5 16th to fall completely out of contention.
Koch bogeyed the par-4 17th, but she countered with a birdie at the closing hole for her second career victory on the LPGA Tour.
'I am so excited,' said Koch, who won for the first time since the 2001 LPGA Corning Classic. 'You get your first win and that is great, but it is so nice to know you can do it again.'
Icher bogeyed two of her first four holes, but she responded with a birdie at the fifth. She then tallied back-to-back birdies from the par-4 seventh, but stumbled again with a double bogey at the 10th.
The 26-year-old from France came back with a birdie at the 11th and another at the par-3 13th. Icher then birdied two in a row from the 16th, but bogeyed the last for a round of 70.
'I am very happy because I have conditional status on the LPGA and with this top 10 I get to play next week, so that is nice for me,' said Icher. 'This is a wonderful course, very difficult.'
Gloria Park and Tina Barrett tied for eighth place at even-par 288 after matching rounds of 72. Charlotta Sorenstam followed at 1-over-par 289.
Stacy Prammanasudh, Audra Burks and Giulia Sergas were two shots further back at 3-over-par 291. Local favorite Lorena Ochoa managed a 73 on Sunday to finish in a group at 5-over-par 293.