Nadal needed just one hour to defeat Argentine Diego Schwartzman 6-1, 6-2, and cancel out Guido Pella's three-set victory over Pablo Carreno Busta in the opening match of their quarterfinal.
The crucial final set went with serve right up until the tie-break, and Russian Federation held their nerve to close it out in dramatic fashion after fending off a Serbia match point to secure their progression. Rublev and Khachanov saved three match points before winning the tie-break 10-8 to seal a 6-4, 4-6, 6-4 win. Nadal then teamed with Marcel Granollers to beat Maximo Gonzalez and Leonardo Mayer 6-4, 4-6, 6-3 in a must-purchase doubles match to discover about Spain into a final-four conflict with Gargantuan Britain.
"In the past year, we've tried to sit down with the ATP, obviously the situation with the former president wasn't ideal to sit down and try to arrive to a deal", Pique, sitting alongside ITF president David Haggerty, said at a news conference on Sunday at La Caja Magica.
Earlier, Rublev was on fire as he dismissed Filip Krajinovic 6-1, 6-2, before Djokovic levelled the tie at 1-1 with a 6-3, 6-3 triumph against Khachanov to set the stage for the doubles rubber.
Pique said the opinion of players like Nadal and Djokovic needs to be heard.
"I think that in the future we are really open to trying to get a new deal, to make a unique competition, a super event of two weeks and try to find the best time in the calendar".
The Russians are seeking their third Davis Cup title, and first since 2006.
The Russians are in the semis for the first time since 2008 and will have to do it all over again on Saturday when they face Canada who enjoyed a rest day after beating Australia on Thursday. "I never experienced such a moment in my career, in my life".
After his 15th straight Davis Cup singles victory, Djokovic struggled in the doubles, although it was Troicki who squandered most of the chances in the tight tiebreaker, including some during the match points.
Britain advanced past Germany thanks to Kyle Edmund's 6-3, 7-5 win over Philipp Kohlschreiber and Daniel Evans' 7-6 (6), 3-6, 7-6 (2) victory over Jan-Lennard Struff.
In the second set and with the Serbs up 4-2 Djokovic appeared to suffer discomfort from his right elbow, the same place where her reported pain at the ATP Finals last week. "And I let my team down, and I apologize to them". Cramming 25 ties into a venue with only three match courts was always going to be a challenge and teams will insist on changes next year to avoid the situation that saw the last rubber between the U.S. and Italy end at 4.04am. "He could play, but I wouldn't say he's in his best condition, as he said to you guys the other day".