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The Old Lady almost had the lead in the 14th minute when Mauricio Isla slammed at goal but had his shot blocked.
Juve were ahead soon after, though, as Tevez pounced on a loose rebound to fire home.
Federico Peluso doubled the hosts' lead in the 28th minute when he met Tevez's free kick with a bullet header into the top corner.
Juve were all over their opponents and made it three on the stroke of half time as Tevez scored his second with a well-taken goal from inside the area.