Third seed Rafa Nadal was given a stern examination but eventually fought back to shake off Marin Cilic 4-6 6-3 6-3 to also make the last four as a potential final showdown with old rival Federer looms.
The Spaniard will play number five seed Richard Gasquet next after the Frenchman beat Ivo Karlovic of Croatia 6-4 6-7(2) 7-6(6) to keep alive his outside hopes of making next month's World Tour Finals in London involving this year's best eight players.
Federer's semi-final opponent on Saturday will be Jack Sock after the American overcame compatriot Donald Young 5-7 6-4 6-2.
The Swiss was knocked out of his last tournament in Shanghai in his opening match but has been on decent form back home.
The first set against Goffin flew by with Federer at his clinical best, taking the one break point on offer while saving two on his serve with some sumptuous shots mixed with the careless errors that have crept into his game in recent years.
The Belgian thoroughly deserved to level in the second and Federer had to shift gears to race through the final set, with the extra backing of his home crowd a definite factor.
Injury-plagued Nadal, who only managed one winner to Cilic's 12 in a first set dominated by a disputed line call, has endured a poor season by his standards but wants to end the year with a bang at the Tour Finals.
The Spanaird's battling Basel performances suggest his best is not far away, although he is not there yet.
Cilic sent down nine aces to Nadal's one while the rest of their statistics were relatively well-matched, Nadal only winning thanks to his age-old trick of wearing down his opponent from the baseline in his third straight three-setter.
(Writing by Mark Meadows; Editing by Ken Ferris)
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