Berdych and the German followed Serena Williams on to court in front of a packed crowd of lucky punters who bought tickets the day before for a hastily arranged extra day of matches to clear the backlog after rain scrambled the schedule.
It is just the fourth time since the tournament started in 1877 that the weather has forced organisers to throw open the doors on what is traditionally a rest day for the players. The last time was in 2004, the first in 1991.
"To play on Sunday, on this Centre Court, I think it is very special," Berdych, 30, said in a court-side interview.
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"I am one of the guys that really love traditions ... it is just the fourth time in such a long history of the championship that we are playing on the middle Sunday.
"I get a chance to play, I get a chance to play on Centre Court, so it can't be better than that."
As a permanent fixture of the top 10 since 2010 and a runner-up at Wimbledon, losing to Rafa Nadal in the same year, Berdych knows class when he sees it and heralded his 19-year-old opponent, seeded 24, as a future grand slam winner.
"He is definitely the guy are we going to hear about a lot," he said of Zverev, who has equalled his best slam result after also reaching round three of the French Open.
Zverev dismissed any pressure from being talked up as a possible future number one.
"There's been a million future number ones that never got to number one. There's other guys right now who want to become number one after Novak," he told reporters.
Berdych will face Jiri Vesely in an all-Czech fourth-round clash on Monday after Vesely beat 31st seed Joao Sousa of Portugal 6-2 6-2 7-5.
(Reporting by Alison Williams)
