The Belarusian started impressively, breaking her opponent's serve in the first game of the match.
However, Hantuchova showed some fight to immediately break back before failing on her serve again to gift Azarenka the advantage.
Despite a couple of nervous moments later in the set, Azarenka managed to find a third break of serve to win the opener 6-2 and make Hantuchova's task even more difficult.
It was Hantuchova who started the second set the better and the 30-year-old was gifted a break of serve when Azarenka, the second seed in the tournament, double-faulted at a crucial stage.
Hantuchova's joy didn't last long though as Azarenka secured breaks in her rival's next two service games.
The change in momentum clearly affected Hantuchova, meaning Azarenka could afford to hand a break of serve back before claiming a 6-3 win in the second set.
The victory means that she has qualified for the semi-finals in New York for only the second time in her career.