The No 2 seed almost suffered a shock second-round defeat but he showed great resolve to come from behind to progress over five sets.
Zverev has never been past the fourth round of a Grand Slam and when he crashed out of the Australian Open to Hyeon Chung in January, Federer offered him a crucial piece of advice.
Federer told the 21-year-old a tale from his younger years which provided inspiration to bounce back stronger at Roland Garros.
And after Zverev’s latest success, he explained that the chat with his Swiss counterpart has helped him relax about rushing his career on too quickly.