The Swiss world number three had not lost to a teenager for nearly 10 years since Andy Murray beat him in Cincinnati in 2006, which highlights Zverev's considerable potential.
Yet the defeat means the 34-year-old Federer will be going into Wimbledon, seeking his eighth title, in the rare position of not having won a tournament this season.
"I feel pretty good. It's unbelievable to get a win against Roger, especially on grass," Zverev said.
News that makes sense
Your trusted source for staying up-to-date with the world around you. Get free daily news updates and analysis, straight to your inbox.
He now has Halle's second all-German final to look forward to on Sunday against Florian Mayer, a surprise 6-3 6-4 winner over another young gun, Austrian third seed Dominic Thiem.
"It's nice with that kind of match going into Wimbledon and obviously into the final here as well," said Zverev. "Don't forget that that final is a very big match for me as well."
World number 38 Zverev, who lost to Federer in their only previous meeting in May, dropped just four points on serve in the 39-minute opening set, blasting 14 winners as he took the tiebreak 7-4.
Federer earned a break of serve at 5-5 with a beautiful dropshot in the second set to restore parity but Zverev, the son of a former Russian player with the same name, responded strongly to dethrone the reigning Halle champion.
The 32-year-old Mayer, now down to 192 in the rankings, cashed in on Thiem appearing a little weary after his recent heroics as he won in 66 minutes.
According to the ATP, he is the lowest-ranked tour-level finalist since No. 240 Nicolas Mahut won in 's-Hertogenbosch three years ago.
(Reporting by Ian Chadband, editing by Pritha Sarkar)
