Wambach scored three times in the first 29 minutes against South Korea on Thursday night to break Hamm's mark of 158 international goals.
Wambach got her 159th in the 29th minute on a line-drive header that ripped into the twine in the back of the net off a corner kick by Megan Rapinoe.
The 33-year-old forward blew a kiss into the crowd and then was mobbed by teammates.
In first-half injury time, Wambach added a fourth for the night.
Her first goal came on a shot in the box past South Korean goalkeeper Kim Jung-mi in the 10th minute. The second came nine minutes later in the friendly on a flicking header.
Lauren Cheney set up the first two goals on crossing passes.
Wambach's fourth goal was an easy tap-in off Alex Morgan's setup.