The Belarusian 16th seed was challenged by Japan's Misaki Doi before progressing 6-7 (3-7) 6-4 6-1 on Grandstand.
Azarenka, a two-time finalist at Flushing Meadows, has endured a frustrating season derailed by foot and knee injuries.
As such, her match with Doi was just her ninth at tour or major level since the Australian Open and Azarenka said she fought her own mental demons to progress.
"Well, I'm my own toughest opponent. So I talk to myself. I curse at myself. I pump myself up," Azarenka said.
"Whatever it takes to do, I don't really give a damn how it looks really because when I'm in the moment I need to be me and I need to do me.
"Whatever helps me to be out there and fight and give my best on every single point, that's what I'm going to do."
Azarenka was none too pleased when asked if she was 100 per cent fit, responding abruptly: "I'm so tired of answering this question. What is 100 per cent physically?"
On her disjointed 2014 season, Azarenka said finding rhythm on court was a tougher challenge than if she was playing every week.
"I think coming back from not playing in general is always tough because you need to get that momentum. You know, I've been working hard on my body," she continued.
"I feel like I'm improving in every aspect. Sometimes what it is, it's challenging to get the rhythm because your physical ability raises up and your tennis has to catch up.
"So during the tournament it's sometimes a battle to do that. But I just take that as it happens.
"I feel like I'm working on the right things, you know.
"And the most important for me fighting-wise is just to enjoy my time on the court. You know, no matter how hard it is or what's going on, I just need to enjoy.
"I need to have that passion. I do play with passion. And I think I have a little bit of extra motivation in a way that I didn't play in a while."
Next up for Azarenka is American Christina McHale, who the Belarusian double-bagelled in Doha last year.