Santos went ahead three times in the match and the visiting Eagles pulled level three times but were unable to muster a deciding fourth goal as they played against 10 men for the final 20 minutes.
Defender Felipe Baloy was sent off for holding back a forward by his shirt, his second bookable offence, with the score 2-2.
Ecuadorean Cristian Benitez put 10-man Santos 3-2 up with a superb shot from the middle of the box in the 74th minute.
However, Enrique Esqueda's diving header at close quarters with five minutes remaining plus four added made for a nail-biting finish for fans of both sides in a packed Nuevo Estadio Corona in Torreon.
The scoring began early with two-goal Colombian striker Darwin Quintero putting Santos ahead in the second minute.
Uruguayan Vicente Sanchez equalised with a well placed free-kick on the hour but from the restart, Quintero raced into the America box on the right and rifled a shot high into the net between keeper Guillermo Ochoa and his left hand post.
America, one of Mexico's biggest and most successful clubs who had surprisingly lost the first leg 2-1 at their Azteca home in the capital, equalised again in the 66th.
Argentine-born former Santos and Mexico striker Matias Vuoso leapt feet forward to get a touch and turn a waist-high left cross into the net.
The match was an example of the entertainment to be had in Mexican football with two teams totally committed to attack and plenty of goalmouth action.
Build-up was quick rather than elaborate and there was a string of missed chances and good saves by Ochoa and opposite number Oswaldo Sanchez.
Santos go into the final, played over two legs this coming week, against the winners of the other semi-final between Pumas UNAM and Monterrey who drew 0-0 in the first leg in Mexico City on Thursday.
