Federer, a five-time champion in the city of his birth, played a second-set tiebreaker to perfection against the 22-year-old.
Seventeen-time major winner Federer also strengthened his position for a place in the eight-man World Tour Finals starting in London in 10 days.
He stands provisional seventh as he heads into a Saturday semi-final with Canadian Vasek Pospisil, who beat Ivan Dodig 7-6 (13/11), 6-4.
Federer could qualify for London if he wins a sixth title in Basel on Sunday, according to ATP calculations.
The Swiss great improved his record to 18-1 against players born in the 1990s, with his only loss in that category coming in Hamburg against Argentine Federico Delbonis this year.
Federer was pleased to be finding some consistent from after one of the poorest seasons of his career.
He began with a wobble on Friday and was forced to save five break points in his opening service game against the Stockholm champion from last week.
"It was very important to win in two sets. There were a lot of free gifts out there in some games," said Federer.
"When I saved three set points (second set) I just told myself to play one point at a time and hope to get there. I broke him (for 5-5) and that made it difficult for him. I was able to come through well in the tiebreaker.
"It always feels good to win at home," added Federer, whose lone title so far came in the summer in Halle.
Top seed Juan Martin del Potro won his 300th career match as he marched into the semi-finals with a 6-4, 6-4 win over Paul-Henri Mathieu.


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