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Norrie has never beaten Zverev.
Dan Evans got the team off to a winning start when he beat Germany's Philipp Oswald in the first game of the match.
The pair's third meeting was won by Zverev.
The British number two, Evans, defeated Jan-Lennard Struff in the first game of the series.
Evans said that he didn't expect to play well.
Kevin Krawietz and Zverev will play the deciding doubles against Jamie Murray and Joe Salisbury.
The first match of the year is never going to be the best match of your life, said Zverev after his win over Norrie. I'm pretty happy with my work. We're here to win.
16 countries are competing in the third edition of the ATP Cup in four groups at two venues in Australia.
Russia's world number two, Daniil Medvedev, was defeated by France's Ugo Humbert.
After Roman Safiullin had beaten Arthur Rinderknech in three sets in the opening singles rubber, world number 35 Humbert won.
The deciding doubles tie was won by Medvedev and Safiullin.
The United States beat Canada in the other tie.
