The Argentine striker broke the deadlock after 20 minutes after a supplying the finishing touch to a sweeping Nice counter, controlling a fine flick from Christian Bruls before firing into the corner.
Timothee Kolodziejcza then went close to a second goal for the visitors, before Salomon Kalou worked the goalkeeper with a low strike at the other end.
Just before the break Nice doubled their advantage thanks to another ruthless counter, with Bruls and Cvitanich combining again to deadly effect in the penalty area.
Lille pressed for a response in an improved display after the break but struggled to create in the final third, with Ronny Rodelin and Kalou guilty of overplaying on numerous occasions.
Idrissa Gueye then fired just over in the closing stages to sum up a frustrating afternoon for the hosts, with Nice holding firm to claim all three points.