Universidad, who won the Copa Sudamericana six months ago, pushed for the win in Asuncion, but Libertad managed to hold the visitors at bay.
Libertad took the lead in the seventh minute of the game, when Victor Caceres converted a Luciano Civelli cross from the left.
Eleven minutes after the interval, Universidad equalised thanks to a long-range strike from Argentinian midfielder Gonzalo Lorenzetti. The ball deflected off a Libertad defender, leaving keeper Rodrigo Munoz with no chance.
Universidad head coach Jorge Sampaoli was pleased with the way his team responded to going behind.
"After the early goal, the team went for the equaliser. However, it was not easy for us to settle down on the field because Libertad had too many defensive players," Sampaoli told reporters in Asuncion.
"The draw is important, but the tie will be so close. We are two even teams and we must be very careful. If we don't play intelligently, we will have a lot of problems," Sampaoli added.
Meanwhile in Rio de Janeiro, Brazilian sides Vasco da Gama and Corinthians played out a goalless draw.
There was little to cheer about for the fans at the Estadio Sao Januario as the sides played out a low-quality game.