Chemistry - Why does zinc plate copper in silver penny lab

Electricity is involved: the copper (well, copper plated zinc in the US) penny is in direct contact with the zinc, forming a short-circuited connection. Forcing the plating action "backwards" (copper being more electronegative than zinc) requires current.

Try the same experiment but with a separator, such as a piece of filter paper, between zinc and copper; there should be no plating.