The 21-year-old defeated Mladenovic 6-3, 6-4 in the opening match of her title defence on Saturday (local time).
Kyrgios went into the tournament on the back of winning the Mexico Open.
Mladenovic will have the chance to beat defending champion Osaka for the second time in three weeks after defeating Zheng Saisai.
Her rankings will improve even more given she was a first round casualty here a year ago but the big question is if she has the wherewithal to push Venus.
"Honestly, I'm over that now", Kyrgios said, adding that he was mentally ready for his Indian Wells opener but just didnt' play well. "I'm really pleased I could win in two sets". Afterward, Djokovic went over to greet former No. 1 Pete Sampras, who sat courtside.
"I had to undergo surgery and a lot of things happened". I tried too hard in the first set to impress him. "He was the one that was really aggressive and dictating the points from back of the court for entire first set".
"It was such a weird match, to be honest".
"Then at the start of the year, I had a little strain on my thigh and I could not play in Brisbane".
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Having made it as far as the semi-finals last season, Venus Williams was one of the risky floaters in the draw and she proved her mettle by defeating the Australian Open runner-up and in-form Petra Kvitova in the previous match. "I just love the battle". "Novak said he is pain-free and I knew he would return to his best, although it did surprise me how quickly he managed to do that". She's seeking her 50th career title. "He's got all the different options how to win points".
Germany's Angelique Kerber enjoyed a sweet victory over Yulia Putintseva.
"For me, it's not a dramatic change", Osaka said.
The three-time victor of the tournament in the Californian desert was under the impression that the match started at 8.00pm and not at 6.00pm. which was the official time when it was supposed to get underway.
Danielle Collins, Belinda Bencic, Anastasija Sevastova, Anett Kontaveit, Julia Goerges, Aryna Sabalenka and Lesia Tsurenko also won through.
There were several upsets on Day 4 of the combined ATP-WTA event.
Two-time Wimbledon champion Kvitova, who was runner-up to Naomi Osaka at the Australian Open in January, also reached the final in Dubai last month.
The eighth seed will meet red-hot Russian Natalia Vikhlyantseva in the third round after the qualifier crushed Spaniard Carla Suarez Navarro 6-2 6-0.