The Swiss star lost only one point on his first serve on his way past the Frenchman in just 54 minutes as he seeks his seventh title of the year.
Fededer, who has now won 32 of his last 33 matches, will next face French wildcard Paul-Henri Mathieu, who continued his unlikely run as he beat Bulgaria's Grigor Dmitrov 7-6(2) 7-6(4).
There was nothing to choose between the two players in either set, with the pair swapping breaks in each set, but it was world number 101 Mathieu who came out on top to earn a probable semi-final against the world number one.
Richard Gasquet made his way into the semi-finals, the French third seed beating Russian sixth seed Mikhail Youzhny 6-2 7-6(5) to earn a spot in the last four against second seed Juan Martin del Potro, who beat South Africa's Kevin Anderson 3-6 7-6(3) 6-2.
Gasquet, the world number 13, ran Youzhny ragged in the opening set, converting two of the nine break points he earned while never looking threatened on his own serve.
Youzhny upped his game as he fought back hard in the second set, with the players trading breaks as they headed to a close-fought tie-break, but it was Gasquet who held his nerve to claim the match and boost his hopes of qualifying for the ATP World Tour Finals in London.
Nicolas Almagro's chances of making next month's World Tour Finals in London were dealt a blow when he was beaten 6-3 7-5 by top seed and Spanish compatriot David Ferrer in the quarter-finals of the Valencia Open.
Almagro, seeded sixth at the indoor hardcourt event, did not win a game on the Ferrer serve but lost his own twice as he slipped to a 12th defeat in 12 career meetings with the world number five.
"I managed to get a lot of my first serves in and kept that up for the whole match," said Ferrer who has already qualified for the Tour Finals.
"It was a very balanced affair and I felt I was very consistent and maybe at the end of the second set his level tailed off a bit and I was able to take advantage," the 30-year-old added in an interview with Spanish television.
Ferrer, like world number 12 Almagro a double champion in Valencia, will play Ivan Dodig on Saturday for a place in the final after the Croatian qualifier upset compatriot and seventh seed Marin Cilic 6-2 7-6.
Cilic needed a win against 110th-ranked Dodig to boost his slim hopes of making it through to the Tour finals but came up short in the pair's first meeting on the ATP Tour.
Alexandr Dolgopolov of Ukraine won the first eight games of his quarter-final against Marcel Granollers before completing a crushing 6-0 6-2 victory over the defending champion to set up a semi-final against Juergen Melzer.
Austrian Melzer, making his debut in Valencia and chasing a fourth career title, saw off promising Belgian David Goffin, 10 years his junior, 7-6 6-4.
Former world number one Rafa Nadal announced on Thursday he had pulled out of the Tour Finals as he continues his recovery from a knee injury that has sidelined him since Wimbledon in June and dropped him down to fourth in the rankings.
Nadal's withdrawal secured Juan Martin del Potro's place in London and there are two berths still up for grabs.
Players including Jo-Wilfried Tsonga and Janko Tipsarevic, who pulled out of their first-round matches in Valencia with injuries, and Gasquet and Almagro are also in contention.
As well as Del Potro and Ferrer, Novak Djokovic, Federer, Andy Murray and Tomas Berdych are already through to the Tour Finals.
Next week's Paris Masters will be the final chance for the remaining hopefuls to seal their spot at the November 5-12 event in London.
ATP Basel quarter-finals
1-Roger Federer (Switzerland) beat Benoit Paire (France) 6-2 6-2
2-Juan Martin del Potro (Argentina) Kevin Anderson (South Africa) 3-6 7-6(3) 6-2
3-Richard Gasquet (France) beat 6-Mikhail Youzhny (Russia) 6-2 7-6(5)
Paul-Henri Mathieu (France) beat Grigor Dimitrov (Bulgaria) 7-6(2) 7-6(4)
ATP Valencia quarter-finals
1-David Ferrer (Spain) beat 6-Nicolas Almagro (Spain) 6-3 7-5
Alexandr Dolgopolov (Ukraine) beat Marcel Granollers (Spain) 6-0 6-2
Ivan Dodig (Croatia) beat 7-Marin Cilic (Croatia) 6-2 7-6(6)
Jurgen Melzer (Austria) beat David Goffin (Belgium) 7-6(7) 6-4