The win by the Spanish third seed also settled the field for the eight-man season wrap-up in London from November 15, with Japan's Kei Nishikori and David Ferrer of Spain taking the last two spots.
Federer, Nadal, World No. 1 Novak Djokovic, Andy Murray, Stan Wawrinka and Tomas Berdych make up the World Tour Finals field.
Earlier in the quarterfinals , top seed and six-time champion Roger Federer held off David Goffin 6-3, 3-6, 6-1 to win a re-run of his 2014 final victory over the Belgian.
In another last-eight clash, Nadal, the third seed, scored a hard-fought 4-6, 6-3, 6-3 victory over Marin Cilic, his third three-set victory this week.
The results:
Semifinals: Rafael Nadal bt Richard Gasquet 6-4, 7-6(7).
Quarterfinals: Roger Federer bt David Goffin 6-3, 3-6, 6-1; Jack Sock bt Donald Young 5-7, 6-4, 6-2; Rafael Nadal bt Marin Cilic 4-6, 6-3, 6-3.— AFP