America had topped the Apertura league standings after 17 rounds but needed an 89th-minute goal from Aquivaldo Mosquera to secure a draw away to Tigres, who qualified for the finals in eighth position.
Tigres had not lost at home since October 5 heading into Sunday's quarter-final first leg but the Monterrey-based club suffered an early blow when Juan Carlos Valenzuela glanced a header into the net from a corner to give America the lead in the 14th minute.
The hosts hit back just after the half-hour mark, however, when Alan Pulido superbly volleyed home from the penalty spot after a whipped left-wing cross by Jorge Torres Nilo.
The visitors could barely gather themselves before Tigres hit the front as a corner was headed down to Guido Pizarro and the 23-year-old midfielder thumped the ball past America goalkeeper Moises Munoz.
But Tigres were denied an impressive victory in the penultimate minute of regulation time when Mosquera flung himself at a hopeful cross and his outstretched leg lifted the ball over Enrique Palos for the equalising goal.
In Toluca de Lerdo, the home side set up a three-goal lead over Cruz Azul ahead of next week's second leg with a 3-0 result.
Oscar Rojas, Pablo Velazquez and Francisco Gamboa scored for Toluca, while in the other two matches on Sunday, Morelia recovered from 3-1 down to draw 3-3 with Leon and Santos Laguna held on for a 3-2 win away to Queretaro.
