Mladenovic's 94-minute victory booked her a blockbuster clash with Australian Open champion Osaka after she upstaged the Japanese star at the Dubai Tennis Championships in February.
She said it was the first time she had felt the pressure of defending a title.
"It's a thrill to see someone I looked up to when I was a kid", said 31-year-old Djokovic.
Kvitova fired 10 aces, but also had 10 double faults and while the Czech fired 38 winners to Williams's 15, her 56 unforced errors were more than double the American's 25. "You never know what's going to come off her racket", Williams said in an on-court interview. I really didn't have any other choice because she was playing so well and serving so well. "But now, I think maybe I'm just grateful for everything, and the hard work that I did finally paid off, and I'm just happy".
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.
World number seven Nishikori was not at his best, with the left-handed Mannarino's flat groundstrokes neutralising his attacks and the Frenchman seemed to be heading for victory when he served for the match at 6-5. Djokovic had to dig deep, however, when Fratangelo battled back to lead 5-4.
M5 snow and ice warning in place until 10am
Cloud will increase from the south-west later today with rain arriving in parts of Munster and south Connacht towards evening. Met Office has issued four weather warnings for snow, ice and very strong winds across Co Armagh in the coming days.
He couldn't muster a match point and double-faulted on break point and that was enough of a window for Nishikori. I think maybe from this perspective, I could have, should have made a different decision, but I believe it also taught me some valuable lessons that helped me to create awesome results in the next seven, eight months and get from 22 in the world to No. 1 in the world in less than six months.
Williams pulled off the unlikely comeback despite failing to produce a single ace although she said her varying serve speeds were "what I needed to do". The ninth seed rallied from a second-set loss to win 6-3, 4-6, 6-0 in an hour and 41 minutes.
Coming off an impressive title win in Acapulco, Kyrgios went down to German veteran Philipp Kohlschreiber 6-4 6-4. Yet the second proved more of a challenge as the German saved four break points in his first service game, then used his momentum to break for a 3-1 lead.
Next up for Barthel is a meeting with either Estonian Kaia Kanepi or countrywoman Julia Gorges, who play their second-round match later on Saturday.
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.