The Argentine forward, who has now scored in their last three league games, pounced on a defensive error in the 29th minute to cancel out Freiburg's third minute lead through Lucas Hoeler.
The 28-year-old old then flicked in a cutback from Lars Bender to put the visitors ahead three minutes from halftime.
Nadiem Amiri gave the visitors a two-goal cushion with a powerful shot just past the hour but Freiburg supersub Nils Petersen cut the deficit with a tap in at the far post in the 72nd to give them hope.
The hosts' comeback, however, was shortlived with substitute Jonathan Tah heading in from a corner four minutes later as Leverkusen, unbeaten in the league this season, earned their third straight win to stay fourth on 12 points, three off leaders Bayern Munich, and one behind second placed RB Leipzig.
Freiburg, who have now gone five games without a win, are in 13th place on six.