OK, looking further into Calvin, here is a more thorough explanation.

Calvin was from a well off family. Not exactly nobility, but according to Bouwsma, his father and mother both had wealth. His Godfather was the local Cathedral's canons, indicating an especial level of piety and church connections of Calvin's father (Parker, John Calvin). Calvin's father also wanted him to become a priest, and set him up with a local noble family, the Montmors, to receive an early education (Bouwsma, p. 9)

When Calvin was 12 he was sent to University at Paris, the typical age for children to receive higher education at the time. In order to pay for all this education, Parker indicates that Calvin's father used his influence with the Cathedral and the Bishop to gain some benefices for the boy (Parker, p. 19).

So the final answer is, Calvin managed to receive a benefice at this age because his father was well connected with his local Bishop and Cathedral, and that he wanted his son John to be a priest from a young age.

Sources: Bouwsma, John Calvin: A Sixteenth Century Portrait, and Parker, John Calvin: A Biography

I can answer to Calvin in particular in a few hours - I'm away from most of my resources at the moment. In the meantime, I believe Bouwsma, John Calvin is an excellent start for Calvin's life.

However, in terms of young benefices, it was a fairly common practice for well connected individuals to receive benefices at a young age. Having a benefice did not mean you had to take a priest's orders, it meant you received the income of the tithes and were responsible for providing a qualified substitute. (See Bernard, Late Medieval English Church, pp. 29-30.) How well this need was administered varied from place to place, but it was a key complaint among reformers - that the person in charge of the spiritual welfare of a town or parish failed to do so, but still took the income.

An excellent example is Thomas Wynter, illegitimate son of Thomas Wolsey, Archbishop of York. Wynter's Wiki article is very thorough, and you can see his list of benefices and positions began at about the same time as Calvin. Wynter was born c. 1510, and had several benefices by the end of 1522 (See also, Pollard, Wolsey: Church and State..., pp. 308-312).