Tsonga, who helped France to victory in Saturday's doubles to keep the best of five tie alive at 2-1, was powerless against Nadal's relentless claycourt game as the world number two claimed his 17th win in 18 Davis Cup singles matches.
The victory gives Spain, who are bidding for a third title in four years and will play champions Serbia or Argentina in December's final, an unbeatable 3-1 lead with only the final singles rubber to be played.
Serbia won Saturday's doubles in Belgrade to maintain their hopes of defending the title they won last year with a 3-2 victory over the French.
On another sweltering day in Cordoba, Nadal followed up his demolition of Richard Gasquet in Friday's opening singles with another commanding display on his favored surface at the Andalusian city's converted bullring.
The 25-year-old lost a grueling US Open final to Novak Djokovic on Monday before flying straight back to Spain and he had little time to adjust to clay from hardcourts.
He did not face a single break point against Tsonga and sealed victory on his first match point when the Frenchman went long with a sliced backhand.
The Mallorca native has not lost a Davis Cup singles since he was beaten by Czech Jiri Novak on his debut in 2004.
