It was a heated tie with a straight red card to each team but the two away goals scored in the second-half by Lanus leave them in excellent shape despite a late Libertad strike.
After a goalless first-half, Lanus opened the scoring on 54 minutes when Santiago Silva drilled Lautaro Acosta's pull back into the roof of the net from the centre of the penalty area.
Nine minutes later, Acosta was brought down just inside the box as he ran on to the ball and Paolo Goltz converted the penalty to double Lanus' lead.
There was a setback for Lanus with the sending off of midfielder Jose Ortiz in the 65th minute allowing Libertad a foothold in the match.
The Paraguayans made use of their advantage on 81 minutes when Gustavo Gomez beat his marker to Rodolfo Gamarra's cross and headed home a lifeline.
More drama ensued in the 89th minute with Libertad substitute Manuel Maciel shown a straight red only seven minutes after being brought on.
Lanus managed to hold their one-goal lead until the whistle and will be favourite to progress when the two teams clash in the second leg in Argentina on Thursday.
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