The world number one, who was expected to breeze through her opening match, was served a blow in a thrilling start to the first-round clash in Paris by going one set down following a tight tie-break.
The 22-year-old committed 28 unforced errors in the early stages of the contest, which allowed her Italian opponent to take control of her service matches and keep the pressure on Azarenka.
The first set was a tight affair and despite Azarenka producing a number of chances to try and force a breakthrough, it was Brianti who took the contest to a tie-break and edged the points to take the lead.
Azarenka continued to struggle against the world number 97, who displayed impressive form to break her opponent and take a four to love advantage in the second set.
The Belarusian professional tried to enforce her game on the contest and her persistence paid off after she managed to draw level and complete a vital comeback to snatch the second set.
The third and final set was a tight affair between the competitors, with both holding serve well and trying to force through a breakthrough but it was Azarenka who edged the set and claimed a spot in the second round.