The severely ill Iraqi baby taken to U.S. Marines at Abu Ghraib prison (search) by her father and then flown to the United States survived a third surgery on her heart and is doing well, her doctors said.

Baby Tabby, who just turned 1, suffered from life-threatening blood tumors called hemangiomas (search) that caused her face to be deformed and excessively swollen. FOX News has been following her story exclusively.

The benign grapefruit-sized tumors were removed in two separate successful operations and Tabby went through a third surgery last week to repair a hole in her heart.

A team of cardiac specialists at the Medical University of South Carolina (search), led by pediatric cardiologist Dr. Jeremy Ringewald, stepped in to perform the heart surgery. Doctors first implanted a balloon to measure the size of the hole in Tabby’s heart, then replaced it with a device designed to close the hole as her heart grows.

The procedure went as planned, and Tabby’s prognosis was excellent. She has one final surgery to remove superficial hemangiomas from her mouth before she can return home to Iraq with her father.

“It actually looks great,” said Ringewald. “I’m really pleased.”

Tabby’s dad, whose identity couldn’t be revealed for security reasons, went to American soldiers stationed in Iraq because he’d grown desperate about his baby girl’s health.

Local doctors told him they couldn’t do anything to cure Tabby’s illness, which was life-threatening in her case: The benign blood tumors could have suffocated her because of their size and location on her neck and mouth.

So he made the dangerous trip from his hometown in Iraq to Baghdad’s now-notorious Abu Ghraib prison — in spite of the prisoner abuse scandal that plagued the facility — in the hopes that the U.S. military could help.

Tabby immediately captured the hearts of Marines from the 4th Civil Affairs Group (search), who made arrangements to have her and her father flown to Charleston, S.C., for the surgeries, with the support of The Hemangioma Foundation (search).

Tabby’s dad has asked to stay anonymous because he’s afraid other Iraqis will misinterpret his appeal for aid from Americans and mistakenly think he’s helping in the U.S.-led war in Iraq.

But he isn’t shy about his gratitude to Americans for saving his daughter’s life — a baby girl who wasn’t supposed to see her first birthday this month and who now has her whole life to celebrate.

Click on the video box at the top of this story to watch a report by FOX News' Jamie Colby.

FOX News' Jamie Colby and Catherine Donaldson-Evans contributed to this report.