
Second seed Nadal and number three Australian Open winner Djokovic produced Tuesday victories to move through a day after four-time winner Federer was toppled in the opening round by Andy Murray.
Nadal expressed relief after putting a form collapse a fortnight ago out of mind with a defeat of German Philipp Kohlschreiber 3-6, 6-1, 6-4.
Third-seeded Serb Djokovic won the battle of the Balkans against Croatian teenager Marin Cilic 6-4, 6-3.
Federer, meanwhile, was analysing what went wrong in his loss to Murray after winning the first set but falling victim of a faulty forehand all evening.
The Swiss will make his way to New York for Monday's sold-out exhibition with Pete Sampras at Madison Square Garden before the start of the first Masters event of the season next weekend at Indian Wells, California.
Federer now stands just 400 ranking points ahead of Nadal, with a weekend title victory by the Spaniard enough to put him just 100 points adrift.
Nadal, always respectful of his Swiss rival who has dominated at number one for four years, gave Federer the benefit of the doubt.
Nadal said he could relate to the three-set loss suffered less than 24 hours earlier by Federer, playing for the first time in a month an not on his best game.
"It was impossible that Roger could win every single week like has has done over the past four years. The level in tennis is very close.
"If you are not on your best game all of the time, you can lose," he said.
Nadal dropped the opening set as Kohlschreiber sprang an early surprise as the Spaniard lost five games in succession.
But Nadal returned the favour in the second set and traded breaks with his opponent before reaching the second round and a date against a Russian qualifier.
Djokovic looks to have finally found form after failing to impress in the post-Australian Open period. He withdrew midway through a Davis Cup match and won just one match in his next event.
"I had a good run here in 2007 into the quarter-finals," said the winner. "Things are different now. Everyone wants to beat me.
"I like the role of favourite and I'm now back on my favourite surface."
The Serb improved to 9-2 this season as he beat 39th-ranked Cilic, who stood 79th at the end of last season.
Sixth seed Andy Roddick made a winning Dubai debut as he beat former number one Juan Carlos Ferrero of Spain 6-2, 6-4 in a battle of ex-Grand Slam champions.
The big-serving Roddick conceded just 11 points on serve, firing 18 aces.
Czech eighth seed Tomas Berdych won his opener over Gael Monfils 6-3, 6-2. But Paul-Henri Mathieu secured a French win as he beat Australian qualifier Joe Sirianni 6-4, 6-4.
By Bill Scott, dpa