Jose de la Cuesta's powerful header from Omar Perez's corner just before the hour mark decided Tuesday's second leg in Bogota as both teams finished the match with 10 players.
Morelia had entered the second leg leading 2-1 on aggregate but De la Cuesta's goal ensured Santa Fe advanced on away goals.
After a scoreless first half in Colombia, the hosts resumed action full of vigour and desperate to make an impact with Santa Fe defender Francisco Meza claiming a yellow card in the 47th minute for a reckless lunge.
Morelia's captain Aldo Ramirez was sent off just five minutes later as the Colombian clashed with Santa Fe skipper Perez in an off-the-ball incident.
Wilson Gutierrez's home side took advantage of their extra player in the 58th minute with Perez picking out De la Cuesta at the near post, and the 30-year-old central defender headed the ball home, despite the best efforts on the line by Morelia midfielder Egidio Arevalo.
The visitors were handed an opportunity to get back in the game just two minutes after the goal with Santa Fe left back Luis Seijas kicking out at Dubier Riascos' shin and getting himself sent off.
But Morelia were unable to make a difference on the scoreboard as Santa Fe missed two fine opportunities to extend their second-leg lead in the closing stages.
Carlos Morales almost snatched victory for the Mexican visitors just before full-time but Santa Fe goalkeeper Camilo Vargas' diving save kept the Morelia left back's free-kick kept out of the top corner of the net.
In the other first round play-off on Tuesday, Nacional defeated Oriente Petrolero 2-1 on aggregate after scoring twice on their home turf.
Carlos de Pena led Nacional to victory as he provided the corner for striker Ivan Alonso to level the tie with a header in the 19th minute in Montevideo, while Nacional's left back scored the winner with 16 minutes left when his shot squeezed through the legs of Oriente's goalkeeper Carlos Arias.
