Azarenka needed 100 minutes in order to book her place in the fourth round after beating her French counterpart 6-4 6-4 to keep alive her hopes of a second Grand Slam.
The Belarusian, a two-time semi-finalist at SW19, broke Mladenovic in the third game to establish a 2-1 lead, before holding her serve for the remainder to secure a relatively comfortable first-set advantage.
Mladenovic, ranked 38th in the world, 14 places below her opponent, looked on course for defeat when Azarenka broke her once again in the opening game.
The former Australian Open champion lost her serve for the first time in the match as her opponent drew level at two games apiece.
Nevertheless, Azarenka broke again in the ninth game to move 5-4 ahead and it was enough to secure the win.
She will face Belinda Bencic in the last 16.