Rupali Meshram, 23, said when she heard the goat scream she ran out of her house in western Maharashtra state.
She picked up a stick and hit the tiger, which then attacked her. Her mother, who was also injured, saved her by pulling her inside the house.
They both sustained only minor injuries and have now been discharged from hospital. The goat did not survive.
Ms Meshram took a selfie of her bloodied face soon after the attack, which happened last week but has only just come to light.
A doctor who treated her praised her “exemplary courage” in fighting off the tiger, but said she was lucky not to have been bitten by the animal.
Ms Meshram suffered injuries to her head, waist, legs and hands, but they were only superficial and she has been able to make a full recovery.
Because of her head injury she was given a CT scan and kept under observation.
“I thought my daughter was going to die,” her mother Jijabhai told BBC Hindi’s Sanjay Tiwari, adding that she had been horrified to see her blood-stained daughter trying to fend off the tiger with a stick.
A photo of Rupali taken by the BBC shows no obvious signs of injuries, 10 days on from the attack.
Her mother was struck by the tiger near her eye, as she pulled her daughter to safety, but her wounds are healing well too.
They say that they called a forest guard but the tiger had left before he arrived 30 minutes later.
The village is often frequented by wild animals due its proximity to a wildlife park.
“I am a bit worried about returning to my village so soon after an attack like this, but I am not scared,” Ms Meshram told BBC Hindi.