A second-half goal saw them gain a narrow advantage heading into Thursday's game, although the visitors will know that the tie is far from over.
Match preview
Atletico Mineiro cruised through the Copa Libertadores group stage with almost a perfect record, defeating America de Cali and Cerro Porteno twice alongside a win and a draw against Deportivo La Guiara.
The first-placed finish saw them book a round-of-16 tie with Argentinian giants Boca Juniors, and they narrowly progressed as the winners of a penalty shootout, after both legs ended in goalless draws.
As a result, they met Boca Juniors' biggest rivals River Plate in the final eight, and an Ignacio Fernandez goal on the hour mark put them ahead, with Cuca's men holding on despite a red card for Fernandez in the final 10 minutes.
That extended a strong run of form in all competitions for the Brazilian outfit, as they have now won their last 12 of their last 14 games in all competitions, while only falling to one defeat in the Copa do Brasil, with priority firmly placed on league action at that point.
The strong run of form has seen Cuca's men rise to the summit of the Brazilian top flight, now sitting five points clear at the top of the division with an eye-catching tally of 37 points from 16 league outings, having cemented their place with a crucial 2-0 win over second-placed Palmeiras last time out.
They will hope to continue their impressive form with what would be a crucial result on Thursday to confirm their passage, although the Galo will be fully aware that they have plenty of work to do if they are to secure an aggregate win.
They take on a River Plate side who arrive with little to lose, as they attempt to overturn a deficit and cause an upset to advance to the semi-finals.
The visitors' group campaign was not as straightforward as that of their quarter-final opponents, as they finished second in group D with two victories from six games, only narrowly pipping Colombian outfit Junior to qualification.
They were handed a difficult tie with fellow Argentinian side Argentinos Juniors in the round of 16, and after a 1-1 draw at home, Marcelo Gallardo's men pulled out an impressive 2-0 win in the away leg to advance to the final eight, thanks to a Braian Romero brace.
While they were previously going through a tough patch of form domestically, River Plate did bounce back from the first-leg defeat with a 2-0 league win over Velez Sarsfield last time out, with Enzo Fernandez and Romero getting on the scoresheet to boost their confidence.
They now head into the away leg with a tough challenge on their hands, but one that is certainly achievable if they start strongly in Brazil.
Atletico Mineiro Copa Libertadores form:
Atletico Mineiro form (all competitions):
River Plate Copa Libertadores form:
River Plate form (all competitions):
Team News
Atletico Mineiro come into the second leg without attacking midfielder Ignacio Fernandez, who will serve a suspension for the red card shown in the away outing, after he put his side ahead.
They recently announced the capture of decorated striker Diego Costa, but he is not expected to come straight into the side.
Instead, the line will be led by Hulk, who has starred in the Copa Libertadores with six goals and two assists in nine appearances this season, alongside seven goals and five assists in 15 matches in the Brazilian top flight.
Without a league game until next Tuesday, Cuca should not have to worry about resting key players, with the likes of Eduardo Vargas, Matias Zaracho and Jair all expected to feature from the start.
Jefferson Savarino should also earn a start after hitting a crucial brace in the 2-0 win over Palmeiras last time out.
Braian Romero will be the key man going forward for River Plate, having already hit five goals alongside an assist in six Copa Libertadores appearances this season.
He should be supported by plenty of attackers, given River Plate's need for goals, with Julian Alvarez, Nicolas De la Cruz, Bruno Zuculini and Jorge Carrascal all set to start.
Meanwhile, Argentinian veteran Enzo Perez will sit in the midfield, offering vital quality and experience with 26 international caps and spells at Benfica and Valencia under his belt.
Atletico Mineiro possible starting lineup:
Everson; Mariano, Silva, Alonso, Arana; Jair, Tche; Zaracho, Vargas, Savarino; Hulk
River Plate possible starting lineup:
Armani; Casco, Diaz, Martinez, Angileri; Perez; De La Cruz, Zuculini, Carrascal; Romero, Alvarez
We say: Atletico Mineiro 1-1 River Plate (Atletico Mineiro win 2-1 on aggregate)
River Plate will certainly push hard and should not be underestimated, but we expect this Atletico Mineiro side to see out a win thanks to their strong squad and eye-catching run of form.
They may be forced onto the back foot by a River Plate side chasing the game, but should have enough to avoid a defeat on home turf.