Serbia forward Vlahovic signed for Juve late last month in a deal worth an initial 70 million euros ($80.2 million) after bursting onto the scene at Fiorentina.
The 22-year-old showed why he is so highly rated with 12 minutes gone at the Allianz Stadium by racing onto Paulo Dybala's chipped through ball before sending a delicate lofted finish over Verona goalkeeper Lorenzo Montipo.
His 18th league strike of the season puts him level with Lazio's Ciro Immobile in the hunt for Italy's 'Capocannoniere' scoring award.
Zakaria, who arrived on transfer deadline day for 4.5 million euros from Borussia Moenchengladbach, doubled Juve's lead on the hour to give them a great chance of moving into the Champions League places.
Massimiliano Allegri's side started the match one point behind fourth-placed Atalanta, who fell to a shock 2-1 home defeat at the hands of lowly Cagliari in Sunday's early match.