Belarusian Azarenka, the beaten finalist at Flushing Meadows last year, took control after breaking Hantuchova with a superb backhand to go 5-2 up in the first set.
Hantuchova, ranked 48th in the world, made a determined start to the second set though, holding her serve and then going 2-0 up, breaking thanks to well-placed volley.
But Azarenka hit back immediately with a break and that clearly rattled her Slovak opponent, who proceeded to make a series of unforced errors.
