The burly Tsonga had helped France to victory in Saturday's doubles to keep the best of five tie alive but 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 gave Spain, who are bidding for a third title in four years, an unassailable 3-1 lead in the world group semifinal in Cordoba before Fernando Verdasco beat Richard Gasquet 6-2, 6-1 in a shortened final singles rubber.
After losing both singles in Belgrade on Friday, Serbia took Saturday's doubles to maintain their hopes of defending the title they won last year with a 3-2 victory over the French.
However, world No. 1 Novak Djokovic, who beat Nadal in a grueling US Open final on Monday, retired from his match on Sunday against Juan Martin Del Potro with a rib and lower back injury to hand Argentina the tie.
Nadal said after his win over Tsonga he preferred to play Argentina in the Dec. 2-4 final as that would mean Spain would be at home and able to choose the venue and surface.
He also reiterated his criticism of the Davis Cup format, which he argues puts too much strain on players already committed to a packed ATP Tour calendar.
"It's always nicer to play at home and the court factor is very important," he said in an interview with Spanish TV.
"Another reason is that I have more friends in Argentina than in Serbia," the Mallorca native added.
On another sweltering day in Cordoba, Nadal followed up his demolition of Gasquet in Friday's opening singles with an equally commanding display on his favored surface at the Andalusian city's converted bullring.
The 25-year-old had flown straight back to Spain after the US Open final and he had little time to adjust to clay from the hardcourts.
He did not face a single break point against Tsonga, converting six of the 17 he created, and sealed victory on his first match point when the Frenchman went long with a backhand, sending the red and yellow-clad home support into raptures.
"You can only experience atmospheres like this at the Davis Cup. It's a very special competition and it's always special for me to play in front of the Spanish public," Nadal said.
"I don't have many opportunities and when I do I try to make the most of them." Nadal has not lost a Davis Cup singles since he was beaten by Czech Jiri Novak on his debut in 2004.
"Rafa just played unbelievable," Tsonga said on the Davis Cup website (www.daviscup.com).
"He was really aggressive, he was everywhere on the court and it was really difficult for me today." Spain captain Albert Costa told local television: "Losing the doubles yesterday made things a bit more complicated but as I have always said beating France 3-0 is very tough.
"The truth is the Davis Cup has been good to us these past few years and we have developed into a very strong team."
