Top seed Nadal extended his winning streak to 13 matches with a 6-2 6-1 demolition of American Jared Donaldson in the Qi Zhong Stadium before world number two Federer, to the delight of his sizeable Chinese fan club, got the better of Argentina's Diego Schwartzman 7-6(4) 6-4.
Nadal, who leads Federer by 2,370 points going into the home straight of a season in which the two old rivals have shared out the game's biggest prizes, was unstoppable against Donaldson and needed only 54 minutes to prevail.
"It was a very quick match in all aspects," Nadal, bidding to end a year on top for the fourth time in his career, said.
"If the year-end ranking happens, it will be, I think, a very important achievement for me.
"With so many years of difference I think it's something very difficult. But there remains work to do."
He last finished the year as world number one in 2013.
Federer shows no sign of giving up the chase but had to battle hard against Schwartzman -- letting slip a break in the first set to get dragged into a tiebreak.
The 36-year-old Swiss always had an extra shot in his locker though and, having taken the opener, broke serve straight away in the second set to move towards victory.
He finished off the contest with his 14th ace, setting up a third round clash against Ukraine's Alexandr Dolgopolov.
"It was a good win, very happy with my first match," Federer said. "I knew he was dangerous. I could have closed the first set out earlier but I started the second set very well."
Spaniard Nadal, who like Federer has won the Shanghai title once, will face Italy's Fabio Fognini next.
Eighth seed David Goffin's hopes of qualifying for the ATP World Tour Finals suffered a blow when he lost 7-6(4) 6-3 to Gilles Simon, while sixth seed Grigor Dimitrov had to save match points on the way to beating Ryan Harrison 3-6 6-3 7-6(6).
Seventh seed Pablo Carreno Busta also went out, losing 7-5 7-5 to fellow Spaniard Albert Ramos-Vinolas.
(Reporting by Martyn Herman; Editing by Ken Ferris)
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