But as he attempted to answer questions in an on court post-match interview with Annabel Croft, there were jeers and boos over his perceived gamesmanship during a crucial moment during the second set tiebreak.
With Federer leading four points to three, Zverev had just served and was about to play Federer’s return when he stopped the exchange and pointed to the back of the court behind Federer where a ball boy had dropped a ball.
The point was replayed and Zverev levelled at 4-4 with his eighth ace of the game.
He went on to take the shootout seven points to five.
“It’s in the rules that we have to replay the point,” Zverev explained to the crowd of more than 17,000 people.
“I’m not sure why you’re all booing,” added Croft. “Because he’s telling the truth. The ball boy dropped the ball and moved across the court and disrupted play and those are the rules so I think you have to be a little more respectful.”
Once the antipathy had died down, Zverev said he had apologised to Federer at the net after the match.
“He told me it was OK and that it was in the rules,” added Zverev. “I’d like to apologise to the crowd. I know that there’s a lot of Roger fans here and he deserves that. He should have that for what he has achieved and what kind of guy he is.
"He should have the most fans in the world and especially here in London where he has so much history.”
Zverev’s 7-5 7-6 victory in 94 minutes was built on solid serving and garish lapses in the normally sleek Federer machine.
The 37-year-old Swiss lost his serve without winning a point when trying to take the first set into a tiebreak.
Federer did get his nose in front in the second set. He broke to lead 2-1 but promptly lost his own serve. From there it was level pegging until the quirky denouement.
Zverev, who is the first German into the showdown at the eight man end of season championships since Boris Becker in 1996, will play either the top seed Novak Djokovic or the fourth seed Kevin Anderson.
Djokovic will start the favourite in that encounter on Saturday night having beaten the South African on seven of their eight meetings. The most recent success was a straight sets demolition in the Wimbledon final in July.
“I’m very proud to be the first German to be in the final for such a long time,” said Zverev. “My team and I have been working very hard for this and I’m pleased to be able to have another opportunity to play again in London.”
Asked about facing Anderson or Djokovic, who beat him in straight sets in the round robin stages on Wednesday, Zverev regained some of his poise.
“When I played Novak a few days ago it didn’t go too well for me … I don’t hope he’ll lose … but maybe there’s a slight preference in the opponent! But it will be the final and I’m happy to be there.”