His ninth title at his hometown event, where he was once a ball boy, has now matched the nine he won at the Halle grasscourt event in Germany.
The 37-year-old delighted his home support to land his ninth Swiss Indoors title, winning 7-6 (7-5) 6-4.
"The results show it as well, so I'm very happy".
Federer clinched minutes after saving a break point, taking his first match-point chance when Copil sent a backhand into the net.
Federer's semifinals opponent will be seventh-seeded Russian Daniil Medvedev, a 6-4, 3-6, 6-3 victor over Greek fourth seed Stefanos Tsitsipas in the day's final match.
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"It would be great to win my 99th career title here in Basel".
"It will be a challenge but I'm excited to see how I feel tomorrow, playing a young guy", said Federer.
Fifth-seeded Kei Nishikori of Japan routed local favorite and top-seeded Dominic Thiem in the quarterfinals at Vienna, Austria, dispatching him 6-3, 6-1 in just 66 minutes.
But a run of five consecutive games for Federer maintained the world number three's spectacular run in this competition.
Medvedev's repeated errors made it easy for his esteemed opponent to wrap up the opening set and there was another break at the start of the second to set the tone. Copil has two after also beating No. 6 Marin Cilic in the second round. Federer stayed focused, breaking back with a smash victor in game seven and taking all the momentum, securing another break at 4-4 and closing the match on own serve in the following game after saving a break point, rattling off five straight games to secure the title in style and lift his 99th ATP trophy in an awesome career.
Anderson, 32, who has never previously finished in the end-of-year top 10, is the first singles player from South Africa to play in the Tour Finals since Wayne Ferreira in 1995.