The US Open is the fourth and the last tournament of the Grand Slam season.
Clijsters ranked 3rd in the world dismissed the Hungarian (ranked 104th) in just over an hour. It was the first time that the two women met.
Clijsters dominated the first set. The score stood at 6-0 in barely 18 minutes. The Flemish tennis diva seemed on course for an easy win, but the nature of the match shifted in the second set.
Arn first went ahead before Clijsters could regain her pose. Clijsters then managed to take a commanding lead and win 7-5.
She now meets Australia's Sally Peers ranked 201st in the world.
Peers created a stir by beating Canada's Aleksandra Wozniak (ranked 54th).
This will be the first time that the two women meet.