Nadal, the third seed, scored a hard-fought 4-6 6-3 6-3 triumph over Marin Cilic, his third three-set victory this week. Sock saw a double-break lead in the second set disappear, but he broke Young at 4-4, then held serve to win the set.
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The third seed retrieved the break in the fourth game, 2-2, with a forehand victor.
Nadal came up against seventh seed Marin Cilic for the first time in over four years and the Spaniard had to dig deep in a 4-6 6-3 6-3 triumph.
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.
The Swiss said that although he had beaten Kohlschreiber a lot, it was always hard against the German who is a tough opponent.
The world No. 3 was playing Russian Mikhail Kukushkin when he produced arguably the highlight of the match in the second game of the second set.
The 29-year-old Nadal s confidence is fast returning after a slow start to 2015 and a few indifferent play in the ensuing months when his ranking slumped to a 10-year low. Unfortunately, I had to play three friends in a row.
During the course of his 17-year career as a professional, Roger Federer has garnered fans from across the globe for his immaculate and graceful style of play.
Gasquet is chasing one of the last two spots remaining in the eight-player finale.
Anything less will send rivals Kei Nishikori and Spain’s David Ferrer to the year-end showpiece.
In another match, 2014 finalist David Goffin of Belgium, hammered by Federer in less than an hour a year ago in the title match, won his opening encounter as he beat Italian Andreas Seppi 3-6, 6-4, 6-4.
Roger Federer and Rafael Nadal both dug deep to progress into the semi-finals of the Swiss Indoors on Friday on a thrilling day of tennis in Basel, Switzerland.
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The fifth-seeded Frenchman saved a match point in the deciding tiebreaker to beat big-serving Ivo Karlovic of Croatia 6-4, 6-7 (2), 7-6 (6).
