Walter Bou, at 4 minutes, Uruguayan Javier Cabrera, at 43, and Gabriel Carabajal, at 52, scored the goals for the home team.
In the domestic tournament, Unión does not dazzle and wanders in the middle of the standings.
However, this Thursday it excelled at the Estadio 15 de Abril and achieved a vital victory.
At four minutes, Bou turned a throw-in into an early goal.
The former Boca Juniors forward received the ball inside the area, controlled it, turned on his own axis, and finished low and across the grass to make it 1-0.
Sebastián Moyano saved the team from conceding the equalizer five minutes before the end of the first half with two consecutive saves.
Shortly after, at 43, Cabrera made it 2-0 with a powerful shot after a quick counterattack.
At 52, Gabriel Carabajal scored the definitive 3-0, also on a counterattack.
Mineiro had more possession but failed to generate dangerous situations.
Unión, on the other hand, retreated after quickly taking the lead and became dangerous by swiftly transitioning from defense to attack.
In the last 15 minutes, the Brazilian team improved and came close to scoring, but Moyano closed the goal with several saves.
With time expired, Moyano, the figure of the match, saved a penalty from Allan.
On the next play, Allan, who had a forgettable night, lost the ball near his own goal and was sent off for committing a foul to stop the opponent's offensive play.
The second leg will take place on February 20 in Belo Horizonte.