Brian de Villiers said on "The Early Show" Tuesday Oudin's dramatic comebacks are a change from her normal style of play.
De Villiers, Oudin's coach since she was just 9, said she usually starts well. However, that hasn't been the trend at this year's Open. Oudin is becoming known for her ability to overcome her opponents, physically and mentally, when all seems lost.
"I think the level that she is playing at now takes a little adjusting, getting used to the pace of the ball, all these girls hit the ball incredibly hard," de Villiers said. "But she's figuring out a way to win and she's doing a great job at it."
De Villiers added Oudin's ability to concentrate has always been her strength.
Oudin, of Marietta, Ga., was the 70th ranked player, but is now being called a "Cinderella" for defying her ranking, knocking out Russian opponents Anastasia Pavlyuchenkova, the fourth seed, as well as Elena Dementieva and former champion Maria Sharapova. And on Monday at New York's Arthur Ashe Stadium, Oudin upset 13th-seeded Nadia Petrova with another come-from-behind win to reach her first U.S. Open quarterfinals.
In tennis, where a number of physical factors -- including height -- apparently play a role in wins, Oudin happens to be shorter than all of the opponents she's beaten.
Oudin told CBS News correspondent Kelly Wallace it isn't about size or even power.
"I've always wanted it," she said, "And it's finally happening."
De Villiers told "Early Show" substitute co-anchor Debbye Turner Bell he thinks she's going to go all the way.
He said, "I put my money on her every time."
Leslie Oudin, Melanie Oudin's mother, said on "The Early Show" her daughter tells her she's just trying to do her best, particularly with the level of serving. However, Oudin's mother said Melanie knows she can rally with the best of the champions at the Open.
"She's very confident in that aspect. And she knows she has a game that she's going to work hard, she's going to fight for it."
Leslie Oudin said she is excited and nervous for her daughter as she advances.
"It's great for her. She's worked that ready for many, many years and it's been a pleasure to watch her," she said. "It's thrilling to see this child have such huge impact on the tennis world now."
Oudin will play ninth seed Caroline Wozniacki of Denmark next in the quarterfinals.