Having started the match with the unexpected tactic of returning Federer's serve from well back beyond the baseline, Zverev experienced more success charging the net and taking the ball early, quickly breaking back to force a first-set tiebreak.
Federer had to wait for Agnieszka Radwanska and Novak Djokovic to see off Timea Bacsinszky and Ernests Gulbis respectively before he got his chance to wow the Centre Court crowd.
It was a similar story in the final set too, with one break proving to be enough for the 18-time Grand Slam champion as he continued his charge for a first Wimbledon title since 2012.
One of the few genuine serve-volleyers left in the game, Zverev stunned Andy Murray in the fourth round of the Australian Open before losing to Federer.
"Good, he's human", the German said.
"I have played him on several occasions now, and he's played me different every time".
Roger Federer and Grigor Dimitrov meet in the fourth round of the 2017 Wimbledon. I'm very happy anyway. In the victory, Federer won 83 percent of his first serve points and 71 percent of his second serve points.
The 13th-seeded Bulgarian built a 6-1, 6-1 lead over Dudi Sela when the 32-year-old Israeli, drained from winning successive five-set fights over Marcel Granollers and John Isner, pulled the plug.
The 35-year-old Swiss has been a model of efficiency breezing through four matches-including a set-and-a-half against Alexandr Dolgopolov, who retired with a foot injury-in just four hours, two minutes.
It is the first time since 2014 at Wimbledon that all the big four have reached the second week, and Federer said: "I think it's great". An elegant backhand gave Federer three set-points and he converted when Zverev netted. Monday's meeting will be their first grass-court clash. We could have nearly played in the Australian Open final against each other.
The Swiss took a hard-fought first set, in which both men broke, in a tie-break and took a further lead early in the second. Mischa is a great guy, I thought we fed off each other. With me, I hoped I was going to be there. I will try to go all or nothing, maybe even more than before. "I'm ready for a tough one but another exciting match because he's a great shot player", Federer said.
However, even Roger Federer can't give birth although that hasn't stopped him thinking about what it might feel like if he could.