Venus Williams booked her place in the third round of the BNP Paribas Open with a stunning comeback victory over Petra Kvitova.
There was disappointment, too, for 2011 victor Caroline Wozaniacki, who fell 7-5, 2-6, 7-5 to 59th-ranked Russian Ekaterina Alexandrova.
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.
Osaka, whose second straight Grand Slam title at the Australian Open in January propelled her to the top of the rankings, was beaten by 65th-ranked Mladenovic in Dubai last month in her first match since she lifted the trophy in Melbourne. Federer finished second at this event last season.
Of the 16 seeds in action, 10 managed to get through.More news: Check your smoke detectors as Daylight Saving Time kicks in
Wawrinka won a taut thriller against 29th-seeded Hungarian Marton Fucsovics 6-4, 6-7 (5/7), 7-5, finally sealing it on his fifth match point after three hours and 24 minutes when Fucsovics lofted a lob long.
World number two Rafa Nadal brushed aside American Jared Donaldson 6-1 6-1 and will next face Diego Schwartzman after the Argentine beat Roberto Carballes 6-3 6-1. In the third round, Djokovic could meet the victor of Germany's Philipp Kohlschreiber and Aussie Nick Kyrgios, last week's Abierto Mexicano Telcel presentado por HSBC champion.
Barthel's compatriot Angelique Kerber was almost flawless en route to a 6-0 6-2 dismantling of Yulia Putintseva, winning 93 percent of her first service points under sunny skies in the Southern California desert. Pella ended the hopes of another Aussie qualifier, Alex Bolt, 7-6 (7/5), 2-6, 6-3.
The first set was particularly even with Osaka winning the decisive break only in the 6th game (4-2) before winning the opener 6-3.
In the women's singles, Osaka began the defence of her Indian Wells Open title with a comfortable win over Kristina Mladenovic of France. "I don't really believe in defending, I believe in getting another one".More news: Captain Marvel Weekend Numbers Surpass $455 Million
For the second straight day, a Williams sister stole the show at Indian Wells.
In what was just the seventh meeting between the two stars, Williams, 38, recorded her third win.
Williams tipped her hat to the two-times Wimbledon champion after the hard-fought contest.
Bouchard save two match points late in the third set but she was unable to stop Flipkens, who claimed her second victory over the Canadian in as many days following Wednesday's doubles triumph. Tournament officials said later she was suffering from a viral illness.More news: Cohen sought Trump pardon, attorney says