By Julian Linden
Williams, back at the U.S. Open for the first time in two years after injury forced her to skip the tournament last year, won her first two matches in straight sets but faces a tricky encounter against the fourth-seeded Azarenka of Belarus.
The pair were drawn to play each other early because Williams was seeded 28th after her ranking plummeted during her long layoff.
"She's had a whole year to prepare and she's been doing really great," Williams said.
"I kinda feel I'm definitely going in as the underdog because she's won more tournaments and she's been doing a lot. I feel like I have nothing to lose in this match."
As the fourth seed, Azarenka had cause to curse her misfortune at meeting the former world number one so early but said she was looking forward to the challenge.
"It's not bad luck. It's a great opportunity," she said.
"She's like a warrior on the court. That's what we're all trying to be. That's what I have to be, really focused myself."
World number one Caroline Wozniacki takes on unseeded American Vania King on Saturday. The Dane has been facing criticism because she has not won a grand slam yet, but has a great chance to go a long way in the tournament with the draw opening up nicely for her.
"I just take one match at a time," Wozniacki said.
"I believe I can beat anyone on a good day. But I have to play on a high level for seven matches and that's not easy."
"I think he's underrated, one of those players that the people are not talking about too much," Djokovic said.
"If he is on the roll, if he feels the ball well, he can be very dangerous because he plays very fast. But if I continue on playing this way, I'm confident that I have a good chance."
(Editing by Larry Fine)