Macnelly Torres's chip into the box came back off the post after eight minutes and Borja was on hand to smash the rebound into the net. It was his fifth goal in the last four games.
The first match last week in Ecuador ended locked 1-1.
"This is thoroughly deserved," fullback Daniel Bocanegra told reporters after the game. "It's a dream come true and now we are off to the World Club Cup which is very important."
A capacity crowd watched Atletico win their second Libertadores, South America's equivalent of the Champions League. They also won the title in 1989.
The home side were the better team throughout and had several chances to consolidate their lead, with Borja and young striker Marlos Moreno both missing golden opportunities in front of a fervent home crowd.
Fellow Colombians Santa Fe won last season's Copa Sudamericana, South America's version of the Europa League.
It is the first time Colombia has held the region's top two club trophies for the first time.