Novak Djokovic and Rafael Nadal both played singles and doubles on Friday, but only the Spaniard was able to lead his team into the last four at the Davis Cup Finals.
Nadal guided Spain to a 2-1 comeback victory over Argentina, while Djokovic couldn't prevent Serbia from being eliminated after a 2-1 loss to Russia.
Andy Murray didn't play again on Friday, but Britain made the last four by beating Germany 2-0.
Spain will make its second straight semifinal appearance after Nadal and Marcel Granollers defeated Maximo Gonzalez and Leonardo Mayer 6-4, 4-6, 6-3 in the decisive doubles match in front of a lively and vocal crowd at the Caja Magica center court.
Guido Pella had defeated Pablo Carreno Busta 6-7 (3), 7-6 (4), 6-1 in the first singles, but Nadal had kept Spain in contention with an easy 6-1, 6-2 win over Diego Schwartzman for his 27th straight Davis Cup singles victory.
"It was a must-win match, nothing else mattered," the top-ranked Nadal said.
Argentina, backed by a boisterous group of fans that at times made more noise than the local Spanish crowd, was hoping to get some payback after it was beaten at home by Spain in the 2008 Davis Cup final, when it was heavily favored against a Spanish team that was without an injured Nadal. Spain also beat Argentina in the 2011 final played in Sevilla.
Argentina made the semifinals for the last time in 2016, when it won its only Davis Cup title.