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Zverev has been managing an elbow injury and had only played three times since mid-March, swiftly departing Masters 1000 events in Miami and Monte-Carlo.
But the German is back in familiar territory on home soil and made light work of lucky loser Ricardas Berankis.
Zverev, who won the tournament in 2017 and 2018, needed just 87 minutes to claim a 6-2 6-4 victory.
"I haven't played much tennis the past few weeks, so I know I'll need to improve for the next match," he said.
"I've had success in the past and I feel good here. I've played well in the practice and hopefully I can do better on the match court."
Fellow seeds Casper Ruud and John Millman each also advanced, albeit the latter only when Guido Pella retired after the Argentine won the first set 6-4 and was 2-0 down in the second.
At the Estoril Open, Marin Cilic and Kevin Anderson will face off in an enticing quarter-final.
One-time US Open champion Cilic has a 6-1 career lead over Anderson, who has fallen to 105th in the world.
Cilic came from behind to beat Nuno Borges 6-7 (5-7) 6-4 6-4, while Anderson defeated Roberto Carballes Baena in straight sets.