On 30 August 1995, Grêmio won their second Copa Libertadores, beating Atlético Nacional on points over two legs.
Both teams had won the tournament once before, with Grêmio taking the honors in 1983 and Atlético in 1989. Grêmio returned to the final in 1984, but were unable to defend their title, losing to Independiente.
They entered the competition in 1995 as Copa do Brasil holders and, after finishing second to Palmeiras in the group stage, advanced with wins over Olimpia, Palmeiras, and Emelec to reach the final. Atlético, meanwhile, entered as Colombian top flight champions and, after also finishing second in their group (to Millonarios) reached the final with victories over Peñarol, Millonarios, and River Plate (on penalties).
Grêmio won the first leg of the final 3-1 on 23 August in front of their own supporters at the Estádio Olímpico, thanks in part to an opening own-goal from Atlético's Víctor Marulanda in the 35th minute. They followed that with strikes from Mário Jardel (43') and Paulo Nunes (55') before Juan Pablo Ángel pulled one back for Atlético in the 72nd minute.
In the second leg, played one week later at Atlético's Estadio Atanasio Girardot, the hosts again opened the scoring with a 12th-minute goal from Víctor Aristizábal. They held the lead deep into the second half, but needed another goal to preserve their hopes of lifting the trophy--the rules at the time decided the winner on points, then by goal differential, so a 1-0 win would draw them level with Grêmio on points, but leave them down a goal on differential.
Then, as Atlético pushed for a second, they conceded an 85th-minute penalty kick that was converted by Dinho to seal the win for the Brazilians. Grêmio returned in 2007, but finished as runners-up to Boca Juniors, while Atlético won the tournament in 2016 over Independiente del Valle.