Brothers Mudasar Hussain, 37, and Ghazanfar Hussain, 42, were convicted at Sheffield Crown Court along with Kamir Ifzal Khan, 37, on Thursday, the NCA confirmed.
Mudasar Hussain and Khan absconded ahead of their trial, and at least one of them has fled abroad.
The NCA said its officers working to locate the two men are now appealing to the public for any information that could help.
Mudasar Hussain was on conditional bail awaiting trial and had surrendered his passport to the NCA as one of those conditions.
An NCA spokesman said that, while he may still be in the UK, it is also possible that he has left the country illegally.
Khan, who was on unconditional court bail ahead of his trial, is known to have fled the country on a flight to Qatar on September 22.
Investigators believe he travelled on to Pakistan.
Of the three defendants, only Ghazanfar Hussain was in court to hear Thursday’s verdicts, the NCA said.
The agency confirmed that Mudasar Hussain was found guilty on Thursday of 12 counts of rape, Khan was found guilty of two counts of rape and one count of trafficking for sexual exploitation, and Ghazanfar Hussain was found guilty of one count of rape.
The CPS said Mudasar Hussain and Khan separately targeted the girl when she was 13 and 14 years old.
The complainant, who is now in her 30s, was groomed and sexually abused first by Mudasar Hussain, then separately by Ghazanfar Hussain and Khan between 2008 and 2010.
Mudasar Hussain, who she knew as “Muddy”, was around 20 at the time.
He plied the girl with and alcohol and, after a few months, took her to a house in Rotherham where he raped her for the first of many times.
The NCA said the girl was abused by Mudasar Hussain “countless times over the course of around 18 months, at the house, in local public spaces and in his car”.
She told officers that Hussain used violence to coerce her, including threatening her with a bat.
The agency said Ghazanfar Hussain – nicknamed “Gucci” – raped the girl when his brother left the UK for a period.
She did not know they were related.
The NCA said the girl met Khan, who was about 20 at the time, when she began frequenting a local takeaway where he worked.
Khan – nicknamed “Kammy” – gave her food, and cigarettes, and took her out on deliveries, leading her to believe that they were in a relationship.
But he raped her during the abuse which lasted around seven months.
According to the NCA, there were a number of times when Khan took her to a house where he asked her to have sex with other men who were present.
She always refused, but Khan took her to a different address where he left her alone with a man, who raped her.
The NCA said that, when Khan returned and found the girl in distress, he told her that he had owed the man a favour.
Ghazanfar Hussain has been remanded in custody ahead of his sentencing at Sheffield Crown Court on Friday.
Mudasar Hussain and Khan will also be sentenced on Friday in their absence.
The trio were arrested as part of Operation Stovewood, the huge NCA set up in 2014 in the wake of the Rotherham child exploitation scandal.
The NCA says Stovewood is the largest law enforcement operation of its kind undertaken in the UK and has identified and supported around 1,150 potential victims, securing 60 convictions against 55 people.
Head of Operation Stovewood Philip Marshall said: “The victim has shown tremendous courage in reporting the predatory grooming, exploitation and sustained sexual abuse these men subjected her to as a child.”
