Federer was pushed to the limits in the final as well Copil forced a tie-breaker in the first set before taking a 4-1 lead in the second.
In the third, Copil kept pace, with Zverev faltering on serve in the 10th game and his opponent taking advantage with a cross-court volley victor to advance amid cheers for the underdog.
The ease of the first set was tempered by a hard second, however, and Federer was finally made to work for his win. Federer though was fortunate to win the set even after making almost 30 unforced errors. Copil stands 2-0 over potential opponent Medvedev but has never played Federer. "I'd like to say a few words to the people on the TV around the world", Federer said."Thank you so much for supporting me this week, it's been a magical week and I can't thank you enough".
Fifth-seeded Kei Nishikori of Japan held off Kazakhstani qualifier Mikhail Kukushkin 6-4, 6-3 in the semifinals at Vienna, Austria.
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.
"I'm very happy. I think it was my best performance this week", Federer said.
"I still can't believe I won, it's been an unbelievable week for me", Copil said. Copil has two after also beating No. 6 Marin Cilic in the second round.
"I was trying to win one or two matches here just to stay there".
The first-set tiebreaker was likely to be crucial given Copil's career record of 8-52 when losing the opening set in top-tier matches.
There was an early warning when Simon broke in the second game and raced to a 5-2 lead. The inspired Romanian's booming serves and lobs created tension St Jakobshalle but the local favourite won five straight games to complete another memorable win.
Federer put the pressure on Simon's serve after battling back from 15-40 down in the 10th game and Simon crumbled with two straight errors.
Nishikori dominated on serve as he beat Kukushkin for the eighth time in eight meetings.