Juventus will be taking on Lazio, Empoli, Bologna, and AC Milan in the next stage of the cup.
Serie A leaders Atalanta are in action on Wednesday against Cesena, while Roma take on Sampdoria.
Reigning Scudetto champions Inter Milan complete the round of 16 when they host Udinese on Thursday.
In Turin, Vlahovic put the home side in front one minute before half-time when he swivelled smartly on a pass to feet from Kenan Yildiz and rolled the ball into the far corner.
Summer signing Koopmeiners then notched up his second goal for Juve with an unstoppable left-footed free-kick from 25 metres out in the 53rd minute.
Vlahovic had the ball in the net twice more for Juve as they pressed forward in search of a third, but was on both occasions denied by the assistant's flag for offside.
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Conceicao eventually made it three on 80 minutes with a whipped finish after cutting in from the right flank and Gonzalez chipped home a fourth with one minute remaining.
(This story has not been edited by staff and is auto-generated from a syndicated feed.)