One of Nadal's main rivals, his compatriot David Ferrer, knows the task facing the challengers.
Earlier on Saturday, Federer claimed third place with a 6-1 7-5 victory against Spain's David Ferrer.
Spanish No.6 David Ferrer looked comfortable as he beat France's Benoit Paire 6-3 6-3 6-2.
Meanwhile, top seed David Ferrer was able to successfully defend his Buenos Aires Open crown in Argentina.
No. 3 David Ferrer won in straight-sets against Japan's Kei Nishikori, cruising to a 6-4 6-2 success.
It took him to 73 match victories this year, equaling the leading mark set by David Ferrer.
There were also victories for Serbia's Janko Tipsarevic, Spain's number four seed David Ferrer and Canada's Milos Raonic.
Another seed to fall on Wednesday was Croatia's Ivan Ljubicic, who was beaten by David Ferrer of Spain.
Djokovic's defeat opened the door for Nadal and the defending champion continued his mastery over fellow Spaniard David Ferrer.
The winner of the Murray-Gasquet match is likely to face world No. 5 David Ferrer in the last eight.
Ljubicic goes on to face David Ferrer in the last four, while Novak Djokovic will play qualifier John Isner.
Sixth seed Lleyton Hewitt had to dig deep to see off Spaniard David Ferrer and reach the last eight.
He lost just five games and didn't face a break point against fourth-seeded David Ferrer, winning 6-2, 6-2, 6-1.
He will play either world No. 5 David Ferrer or Czech Davis Cup winner Tomas Berdych on the second day.
The hosts are currently 2-0 up against a Spanish team without Rafael Nadal, David Ferrer, Nicolas Almagro and Fernando Verdasco.
He also selected David Ferrer, Feliciano Lopez and Fernando Verdasco, with Santiago Ventura, ranked 122nd, travelling as the first substitute.
In Acapulco, Nadal is the No. 2 seed behind countryman David Ferrer, who has overtaken him in the world rankings.
Fifth seed David Ferrer is also safely into the second round after a 6-3 6-4 6-3 win over Belgium's Steve Darcis.
World No. 4 David Ferrer has reached the final of the Copa Claro in Argentina, where he is defending his title.
Top seed David Ferrer won the Valencia Open title with a 6-1 3-6 6-4 victory over Aleksandr Dolgopolov of the Ukraine.
Three places remain up for grabs for the end-of-season event in Shanghai, with David Ferrer likely to take one of them.
In Oeiras, Stanislas Wawrinka upset top seed and world No. 4 David Ferrer 6-1 6-4 to win the Portugal Open on Sunday.
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Model turned actress Brooklyn Decker was there to support her husband Andy Roddick, who lost to David Ferrer in the third round.
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Earlier, champions Spain had secured a 2-0 lead over Israel thanks to convincing singles wins by Juan Carlos Ferrero and David Ferrer.
Lopez's compatriot David Ferrer enjoyed more success in his second round match.
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In Madrid, he was two points from losing to David Ferrer, whom he had beaten, at that point, 14 straight times on clay.
Meanwhile, Federer was also taken to three sets by Andy Murray's conqueror David Ferrer, before eventually fighting back to win 7-5 3-6 6-3.
Next up for Haas is third seed David Ferrer, who came from one set down to defeat Austria's Jurgen Melzer 4-6 6-3 6-0.
The eight players in the Masters Cup field are: Nadal, Gasquet, Federer, Fernando Gonzalez, Novak Djokovic, Nikolay Davydenko, Andy Roddick and David Ferrer.
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