Antonio Mohamed's men went into the return leg at the Estadio Azteca trailing Tigres UANL 1-0 but goals to Michael Arroyo, Pablo Aguilar and Oribe Peralta helped America to a 3-1 aggregate victory and a record 12th national title - surpassing rivals Chivas Guadalajara.
Tigres ended the second leg with just eight men after a total of four red cards were shown by referee Paul Delgadillo.
Joffre Guerron's 64th-minute goal gave Tigres - who finished adrift of table-topping America on goal difference during the regular season - a slender lead on Thursday.
And America set out to erase that deficit early, with Ecuadorian Arroyo levelling the final on aggregate nine minutes before half-time.
Paraguayan defender Aguilar put America ahead on aggregate in the 62nd minute, two minutes before Tigres substitute Hernan Burbano was sent off within a seconds of his introduction, sparking a flurry of red cards.
Tigres found themselves down to nine men three minutes later, winger Damian Alvarez given his marching orders for fighting.
It got worse for Tigres in the 72nd minute as Argentinean goalkeeper Nahuel Guzman saw red for a second yellow card.
And America made the most of their numerical advantage 12 minutes from time, with Mexico international striker Peralta completing the scoring.
America also had a player sent off, substitute Luis Mendoza sent down the tunnel in the 79th minute, six minutes after he replaced Rubens Sambueza.
