Federer, who skipped the entire claycourt season after winning the Australian Open and claiming titles at Indian Wells and Miami this year, will next play defending champion Florian Mayer who beat Frenchman Lucas Pouille in three sets.
The Swiss, who lost his first comeback match in Stuttgart last week, is still lacking some game sharpness and squandered three set points at 5-4 in the first set of an entertaining serve-and-volley encounter.
He persisted and carved out two more, winning the tiebreak by whipping a crosscourt backhand winner on his fourth set point.
Zverev's erratic first serve was a liability and Federer pounced again at 4-4 in the second set to break the German, whose younger brother Alexander is through to the quarter-finals, and served out the match.
World number nine Kei Nishikori's own Wimbledon preparations suffered a setback when he was forced to retire injured for the third straight time at this tournament.
The third seed needed to take a medical time-out against Karen Khachanov to treat a back injury before playing on for a few points and retiring with the Russian leading 3-2 in the first set.
Wimbledon, the only grand slam to be played on grass, starts on July 3.
Khachanov will now play fellow Russian Andrey Rublev, who earlier beat Mikhail Youzhny.
(Reporting by Karolos Grohmann; Editing by Gareth Jones and Toby Davis)
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