Abdul Hameed and Muhammad Shahzad, owners of the two goats, however, refused to sell them.
More than 50 goats from Ahmadpur East, Alipur, Head Panjnad, Khanbela, Channi Goth and Zahirpeer participated in the race.
Other goats either strayed away from the track or failed to start the race on the sound of the horn.
Goats owned by Malik Manzoor, Haji Ahmed and Nazir Ahmed stood first, second and third in a dance competition later arranged at the same venue.
The goats, decorated with jewels and cloth, danced to the beat of a dhol.
Turbans were put on the heads of the five winning goats as a token of appreciation in the concluding ceremony.
Organisers Ghulam Qadir and Malik Abdul Hameed said that they had been arranging the event in Uch Sharif for several years. They said there was no entry fee for the competition.
They added that anyone could bring their goats to the competition.