And in May he can complete a historic "Novak Slam" by holding all four Grand Slams at the same time if he wins the French Open.
Mladenovic, ranked 65th in the world, seized her first career victory over a number one player when she shocked Osaka in the second round at Dubai last month, the Japanese star's first match since her victory in Melbourne.
Nadal, playing his third tournament of a year that started with a crushing loss to Djokovic in the Australian Open final and included an early exit in Acapulco, converted five of his six break chances against Donaldson and never faced a break point himself. Federer finished second at this event last season.
Venus Williams fought back to down third seed Petra Kvitova 4-6 7-5 6-4 and reach the BNP Paribas Open third round on Saturday, while Naomi Osaka got her title defense off to a flying start with a straight sets win over Kristina Mladenovic.
Zheng, ranked 39th in the world, played some solid tennis in the opening set before losing at 7-5, 6-2 in one hour and 34 minutes.
Federer could find himself fighting for a fourth-round berth against fellow Swiss Stan Wawrinka, a three-time Grand Slam champion now unseeded as he continues his return from injury.
Earlier, another American, Madison Keys, blew a late lead to fall 3-6 6-1 7-5 to German Mona Barthel.
Djokovic will play Philipp Kohlschreiber, who is ranked 39th, in the next round after the German beat Nick Kyrgios 6-4 6-4.
Angelique Kerber kicked off her campaign with a comfortable 6-0, 6-2 victory over Yulia Putintseva. Pella ended the hopes of another Aussie qualifier, Alex Bolt, 7-6 (7/5), 2-6, 6-3.
Djokovic sprinted over to the stands to shake hands with his idol, 14-times Grand Slam champion Pete Sampras, immediately after the 7-6 (7-5) 6-2 win. "We always play three-setters, and suddenly, we have been there again and playing until the end, and in the end of the match, she definitely played better than me". "Had some moments where I let go of coaches that were maybe, for the outside people, not a logical step, but for me really the only step", Federer said.
For the second straight day, a Williams sister stole the show at Indian Wells.
An ailing Serena Williams retired from her third-round match while trailing Garbine Muguruza 6-3, 1-0 in a battle of former world number ones.
Williams tipped her hat to the two-times Wimbledon champion after the hard-fought contest. Tournament officials said later she was suffering from a viral illness.