Gustavo Alfaro's Arsenal, who won this title in 2007, worked hard in the first period and managed to wrap up the win in the second half.
Arsenal took the lead five minutes after the interval as a Luciano Leguizamon free-kick was deflected into his own net by the head of Estudiantes midfielder Leandro Benitez.
Another free-kick was the key to Arsenal doubling their lead in the 75th minute as Adrian Gonzalez delivered a ball into the box which defender Guillermo Burdisso headed home.
Arsenal midfielder Ivan Marcone was happy for the victory, saying: "I'm delighted by the job all the team did tonight.
"To us, it was good to take a good lead and not concede goals."
"It was tough in the first half but Gustavo (Alfaro) talked a lot in the break so in the second half we made the difference," he told Fox Sports.
Estudiantes defender Christian Cellay, meanwhile, is sure the team will turn the tie around in the second leg on September 6,
"We have plenty of confidence, although we know it will be hard," he said.
"If we give up, we'll never get over this bad moment."
In Paraguay, hosts Nacional failed to beat Bolivia's Aurora and the 1-1 draw means the visitors have little advantage ahead of the second leg.
Aquilino Villalba put Aurora ahead in the fifth minute with a header.
Paraguayan striker Villalba was sent off seconds before half-time after making an obscene gesture towards the Nacional fans and the home team profited.
Javier Gonzalez equalised 22 minutes after the interval and everything is uncertain ahead of the return game in Cochabamba on September 20.