The michoacanos had taken the lead in the 31st minute and it looked like they were going to hold on it right up until the 86th minute, when Emanuel Loeschbor was called for a penalty.
Dorlan Pabón converted the PK to tie the game 1-1; with Jaguares beating Atlas, the draw would have relegated Morelia.
But the Monarquía’s leading goalscorer, Raúl Ruidíaz, turned into the hero of the game as his 91st minute goal made it 1-2 and kept Morelia in the first division.
Incidentally, the victory also puts Morelia into the playoffs as the 8th seed, as they beat out América and Pachuca on goal difference to claim the final Liguilla berth.
As for Monterrey, they were already assured of a spot in the playoffs going in, so the loss was not too much of a blow for the Rayados.
With the 1-2 win, Morelia reaches 24 points while Monterrey still has 27.
Monterrey: Hugo González, Nicolás Sánchez, Efraín Juárez, Luis Fernando Fuentes (Rogelio Funes Mori 55′), César Montes, Edwin Cardona, Walter Ayoví, Walter Gargano, Carlos Sánchez (Arturo González 73′), Dorlan Pabón, Jonathan Cristaldo (Yimmi Chara 62′).
Morelia: Sebastián Sosa, Enrique Pérez, Gabriel Achilier, Carlos Gerardo Rodríguez, Emanuel Loeschbor, Aldo Rocha, Jefferson Cuero, Andy Polo (Rodolfo Vilchis 27′), Rodrigo Millar (Miguel Ángel Sansores 87′), Gastón Lezcano (Diego Valdés 60′), Raúl Ruidíaz.