After Mladenovic held serve to narrow the deficit to 5-4, the Japanese player faced another break point before wrapping up the match after one hour and 21 minutes.
"Those are the matches I know can help me to get some big results", said Wawrinka, who is now ranked 40th in the world.
That victory gave the Serbian his third consecutive Grand Slam title after last year's Wimbledon and US Open triumphs.
"I've never been a defending champion before, that's new and I was really nervous", said Osaka, who booked a third-round meeting with American Danielle Collins, who was a 6-4, 6-1 victor over Kirsten Flipkens.
The 38-year-old was trailing by a set and double break down when she pulled off a stunning comeback to register a 4-6, 7-5, 6-4 win over No.3 seed Kvitova of Czech Republic in a thrilling clash that lasted almost two-and-a-half hours.
McHale won her match 6-4, 3-6, 6-4 against Anastasia Pavlyuchenkova.
However, the American was unable to close it out, a double fault and a pair of errors handing Djokovic the opening set.
One killed, 33 wounded in blast inside bus station in Kashmir
Inspector General of Police, Jammu , MK Sinha, as quoted by PTI, informed that there was no specific input about such an attack. He also pointed out that he spotted 10 people injured at the scene who were being shifted to the nearby hospital by the locals.
Ranked no.25, the American had an emphatic start of her Indian Wells campaign with a strong 6-4 6-1 win over Kirsten Flipkens.
Meanwhile, world No. 1 Novak Djokovic picked up steam during his second-round match against American Bjorn Fratangelo under the lights on the stadium court as he goes in search of his 74th ATP title.
"I think in the tiebreak I played best tennis of the match, I was really focused", said Nishikori, who opened 2019 with a title in Brisbane and then reached the quarter-finals of the Australian Open.
"To be honest, I was a bit nervous in the beginning, I didn't play my best. I still feel like I have a lot to learn".
But Williams immediately broke back and Kvitova soon found herself serving to save the match. It was just her eighth match of the year.
A tougher test awaits in the third round in Wawrinka, who got past Marton Fucsovics 6-4 6-7 (5-7) 7-5 in a clash lasting nearly three and a half hours.
"I was playing really aggressive", Kerber said. "I think I played better than I did in the previous round", said Gunneswaran. "So it's nice to know that in that sort of situation I can still play and just lift my level".
He'll play Guido Pella, who ended the hopes of another Aussie qualifier, Alex Bolt, 7-6 (7/5), 2-6, 6-3.