Midfielder Javier Cortes broke the deadlock 14 minutes from time to give Pumas a 3-2 aggregate victory following Thursday's 1-1 draw in the first leg of the final at the Morelos for the university team's seventh league title.
The team that launched former Real Madrid striker Hugo Sanchez to fame succeed Monterrey, who won the Apertura title in the first half of the season, as champions.
"I was more nervous than at the birth of my first child," Pumas president Victor Mahbub told reporters.
Pumas took the lead with a 14th minute penalty by veteran former Mexico striker Francisco Palencia but their former midfielder Jaime Lozano equalised 11 minutes later also with a penalty.
The 21-year-old Cortes, a product of UNAM's youth scheme, scored a brilliant winner, weaving past three defenders to unleash a searing shot past Morelia's goalkeeper Federico Vilar.
"Really, that was the move of my life, that was the goal for the championship," Cortes said. "I dared to have a go, I dared to shoot and how good it was to get that goal," he told reporters after the Pumas' lap of honour.
Morelia's "Monarchs", who upset Cruz Azul in the semi-finals, were looking for their second league title.
