"I'd love to see now what kind of results I can have - but it went his way today, this is how it ended".
Copil stormed out of the blocks in the second set, racing into a 3-0 lead before Federer got on the scoreboard, but the Swiss kept a level head to reel his opponent back in before breaking serve to take a 5-4 lead in the second set.
"I still can't believe I won, it's been an unbelievable week for me", Copil said.
"The results show it as well, so I'm very happy".
Federer started his slow recovery with a break for 4-5; he then saved set points to level at 6-all, winning a game in which he double-faulted twice in a row and saved a set point with an ace.
From there Federer really set the tone of the match in the tiebreaker, where the Swiss man raced to a 5-1 lead before earning the set after an hour of hard-fight when Simon erred his backhand wide.
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Red Bull Leipzig has been on a six-match unbeaten run since losing their opening Europa League fixture to Red Bull Salzburg. We don't necessarily need a big victory but the most important thing is winning".
The win was a reversal of the first main draw match of Zverev's career when, as a 16-year-old wild card, he lost to Bautista Agut in Hamburg in 2013.
The world number five is aiming for his fourth ATP title of the season.
The top-seeded Swiss rallied from trailing by a service break in each set against the 93rd-ranked Romanian, whose serve was measured at 243 kph (151 mph) in his opening service game.
"I knew it was going to be hard".
Their first meeting came after Federer amassed 20 Grand Slam singles titles, while Copil has just one career match win at a Grand Slam - in the 2015 Australian Open first round.
Copil again showed his steel with an early break in the second set before Federer made another fightback with an overhead victor to break back in the seventh game.