Wambach scored four times in the first half to break Hamm's record for international career goals with room to spare in a 5-0 victory over South Korea on Thursday night.
The four goals gave the 33-year-old Wambach 160 in207 games, two more than Hamm had in a storied 275-game career that ended in 2004.
Wambach connected three times in the first 29 minutes to break Hamm's mark of 158 international goals, and she added another in injury time to give her a nice round number.
Ali Daie of Iran holds the men's record with 109.
"I can't say how much I look up to Mia and how amazing the record she set was," said Wambach, who was doused with a bucket of water after the game.
After crediting her teammates for her scoring prowess, Wambach said it was a night she will treasure.
"It was a special night," said a soaking wet Wambach. "It was surreal when it was happening. I felt when I missed the breakaway (after the first goal), hey maybe it's not going to happen. But my teammates were relentless putting me in those positions, and it's obvious."
The historic 159th came on a line-drive header that ripped into the twine in the back of the net off a corner kick by Megan Rapinoe.
"I'm just so proud of her," Hamm said. "Just watching those four goals, that's what she is all about. She fights for the ball, she's courageous and she never gives up. Her strength and perseverance is what makes her so great and it's what defenders and opposing teams fear.
"From being her teammate early in her career, I know all she ever wanted to do was win, and she continues to do that. I'm just glad I got to share 158 with her. It was short, but it was fun."
After the record-setting goal, Wambach turned and ran a couple of steps in the direction of the U.S. bench, then stopped as Rapinoe jumped into her arms. The Rochester, N.Y., native was then mobbed by teammates on the field and those who streamed off the bench as the crowd of 18,961 at Red Bull Arena cheered wildly.
After the hugs, Wambach turned to the stands and blew a kiss toward her parents, Judy and Peter.
"My teammates know me super well and at halftime they said: 'You're such an extremist," Wambach said of getting the record. "You are all or nothing. When you want to do something, you just go do it. I am very much like my father in that way."
Other than "perfect ball" Rapinoe quipped, the only thing she said after the goal was "YESSSS!"
"I'm just so happy for her," Rapinoe said. "This was an amazing, amazing accomplishment in way less games, the way she has done it. It's incredible to be a part of it."
Chants of "Ab-bee, Ab-bee, Ab-bee," cascaded through the stadium as officials got the ball and gave it to the U.S. bench.
The four goals in the friendly were the second most by Wambach in an international game, and will allow the spotlight that has followed her in her chase of Hamm's record to finally dissolve.
Her first goal Thursday 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 on plays that Wambach eluded Korean defender Shim Seo-yeon.
Wambach's fourth goal was an easy tap-in after Alex Morgan made a run down the right side and centered the ball to the on-rushing Wambach, the 2012 FIFA Women's World Player of the Year.
Wambach, who was stopped on a first-half breakaway shortly after her first goal, had a chance for a fifth goal, which would have tied her single-game record, but she could not get her head on a cross early in the second half.
"She had her mind set," U.S. captain Christie Rampone said. "She wanted to do it tonight and you could see it. Three goals in less than 30 minutes, an amazing performance by her. It was the best of both worlds, she got to score four goals and then watch the rest of the game and enjoy the day."
Wambach was given a standing ovation by many in the crowd when she was replaced in the 58th minute by Christen Press. Before leaving the field, she exchanged hugs with long-time teammates Rapinoe, Heather O'Reilly and Carli Lloyd and a few other players. As she got to the sideline she applauded the crowd and then hugged her coaches and teammates. The crowd chanted "Abby Wambach" in return.
"It's fantastic, a fairy-tale night," US coach Tom Sermanni said. "She could not have done it any better, just fantastic. She is a great professional . She is in great shape and she was really determined tonight to go out there and break that record, and she did it in great style."
Cheney added the final goal for the United States on a header in the 64th minute.
Goalkeeper Hope Solo made her first start for the United States since having wrist surgery in early March. She faced one weak shot as the ball stayed in the South Korean half most of the game.