In just the third game of the match 23-year-old Azarenka was handed a break to go 2-1 in front by Flipkens, who committed a double fault with the score at 15-40.
Azarenka then earned a double break to go 5-2 up, before serving out to take the opening set.
Belgium's Flipkens provided more resistance during the early stages of the second set as both players held their opening two service games.
However, Flipkens failed to land a number of her first serves in during the fifth game of the set and Azarenka took full advantage by claiming the break, going 3-2 up process.
Then, just as she had done in the first set, Azarenka recorded a double break to open up a 5-2 advantage. She then served out to wrap up the victory on the Arthur Ashe Court.