Lucas Melano scored a brace in the first leg of the round of 16 tie to put his side in a commanding position as 2011 Sudamericana champions Universidad showed very poor form in Buenos Aires and ended the game with nine men.
Former Boca Juniors' Uruguayan striker Santiago Silva put Lanus ahead in the 24th minute by finishing a Diego Gonzalez cross from the right.
Maximiliano Velazquez then set up Melano when he crossed the ball from the left before the striker fired home again two minutes later when he raced from midfield to beat Johnny Herrera.
In the second half, Lanus seemed to sit back but were only waiting for the right time to take advantage.
In the 67th minute, Silva's attempt hit the crossbar and Santiago Acosta followed up to send the ball into the back of the net.
The last 10 minutes saw Universidad lose control as keeper Herrera was shown red for fouling Melano outside the box. Midfielder Luciano Civelli had to replace him in goal as all of the available substitutions had been used.
With six minutes remaining, Universidad midfielder Juan Rodrigo Rojas tackled Jorge Pereyra Diaz from behind and was also shown a red card as his side finished the game with nine men.
Melano was pleased to claim such a convincing victory.
He told Fox Sports: "This is the match we had expected. We all worked very, very well, in all the lines.
"Universidad de Chile were tough rivals but we did our job well."
Silva added: "This result encourages us so does the way we played. Taking such a wide lead against important rivals like Universidad de Chile is very good for us."
Another Argentinian side who won tonight was Velez Sarsfield, who beat La Equidad 2-1 in Colombia.
Velez took the lead seven minutes after the interval when Mauro Zarate's shot on goal and the ball was unintentionally deflected by La Equidad defender Yonni Hinestroza into the back of the net.
The hosts equalised with a 75th-minute header by Wilmer Diaz, following an Ivan Rivas' free-kick, but Alejandro Cabral netted a right-footed shot to give Velez the victory with 10 minutes remaining.
La Equidad midfielder Jonathan Alvarez was shown red three minutes from the end for a tough tackle on Francisco Cerro and will miss the return match.
"We played well tonight. We knew La Equidad's weak point was defense but their attacking skills were good so the result puts us in a very good position," Velez forward Lucas Pratto said.