The two teams had tied 1-1 in the first leg on Wednesday, December 8, in Huanuco, some 350 km northeast of Lima.
Veteran Peruvian striker Pedro Garcia opened the scoring for San Martin with a header off John Hinostroza's cross in the 15th minute. Argentine midfielder Pablo Vitti added a second with a thumping free-kick nine minutes later.
Leon hit back with a 28th-minute penalty converted by Colombian striker Luis Perea after he had been brought down.
"We were a great team, a great squad, that's why we have this happiness. (The final) was tougher than we expected," San Martin's Uruguayan coach Anibal Ruiz said.