The defender benefitted from slack Celtic marking at a Valter Birsa corner four minutes after half-time, as Kaka had in the first period, before Mario Balotelli clinically wrapped a 3-0 triumph with an hour played.
The result was vital for Milan, not only in preserving second place ahead of the San Siro showdown with an Ajax side who shocked Barcelona 2-1, but also in ending a seven-match winless run that brought an angry reaction from supporters at the 1-1 weekend draw against Genoa.
"Next we have the home game against Ajax and one point will be enough for us but once again we will try to win," Zapata told UEFA's official website.
"We were coming into this game after a difficult period but we responded well on the pitch.
"I am very happy with my goal but mostly with the well-deserved victory. We came here to attack and win the game and we managed to do just that."
Christian Abbiati endured some uncertain moments as Celtic asked questions of the visiting defence throughout and the Milan goalkeeper praised his team-mates for keeping their cool amid a typically feisty Parkhead atmosphere.
"I congratulate all my team-mates because it was not easy,” he told UEFA's official website.
"Hopefully this will give us confidence and we can build from here. I am sure we can come out from this difficult situation.
"The win was important for many reasons. It is always difficult to play here. You can hear every Celtic fan singing, but we proved to be a united group."
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