Federer dropped just eight points on his serve and was hardly troubled in a one-sided contest as he converted a decisive break point in the ninth game of the second set to march to victory.
"I got out of the box well, I felt good right away," Federer said. "This is an easier court to play than last week in Stuttgart.
"The ball bounces up higher into my strike zone. I was connecting well on returns and I could read his serve."
Chasing a record-extending 10th title in Halle, Federer will next look to improve his 6-0 head-to-head advantage over Frenchman Benoit Paire, who beat American Steve Johnson 7-5 7-6(5).
World number three Zverev began his grasscourt campaign with a disappointing 6-1 6-4 defeat by Croatian Borna Coric.
The German dropped his serve four times in an erratic display as Coric clinched his 20th match win of the season.
(Reporting by Anirban Paul in Bengaluru; Editing by Alison Williams and Pritha Sarkar)
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