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 ATP 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 (11), 6-4.
Federer could qualify for the ATP World Tour Finals in London for the 12th straight year if he wins a sixth title in Basel on Sunday.
Roger showed great tennis during several periods, even though he had to battle every now and then. He had to fight off five break-balls in his first service game but found his rhythm from there on, showing a great rest of the opening set. Dimitrov broke him early in the second set, Roger falling behind 3-5. He managed to save three set-points and take the set into a tie-breaker - which he clearly decided in his favour.
With his 50th victory in Basel he has now won 50 or more matches at 5 different tournaments (the others being Grand Slams).
"It was very important to win in two sets," said Federer.
"There were a lot of free gifts out there in some games.
"When I saved three set points in the 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.
Date: 25th October 2013, Source: AFP and RF Official
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