The No.2-seeded Azarenka had some struggles on the big points - she converted just three of 14 break point chances - but she never lost serve herself and her match numbers were just cleaner, 20 winners to 20 unforced errors compared to her opponent's 20 winners and 32 unforced errors. At the end of the day the two-time defending champion was too sharp, beating the No.13-seeded Stephens, 63 62.
"I'm happy with the way I played," Azarenka said. "We were very competitive. I know Sloane is a great player, a very tough fighter, and she was holding serve really well. I felt like I had a few chances but she came back strong, so it was important to stay in that zone and try to create another opportunity.
"I felt I was able to do that."
"We had some long rallies and some long games and I didn't convert on some of my break points or opportunities," Stephens said. "It could have gone either way, but I just didn't win some big points.
"But she definitely played some good points. She's steady. She's consistent mentally. Physically she's all in. She's just a really tough competitor. I'm still working on things and trying to get better.
"I'll work on a few more things and hopefully next time will be the other way around."
Azarenka and Stephens' only previous meeting was the semifinals last year - this time, fourth round.
"Both matches - last year and this year - were pretty competitive," Stephens said. "The score doesn't reflect what I guess was out there. I just have to keep working on it and try to do better next time."
Looking ahead to the quarterfinals, there's a very different dynamic for Azarenka now. With Serena Williams and Maria Sharapova's exits over the last 24 hours, and with her record here - she has won 18 matches in a row here and is the two-time defending champion - she's now the clear cut favorite.
The focused Belarusian isn't looking at anything beyond her next opponent, though.
"It doesn't matter. The players who beat those players deserve all the credit because they've been better, so they are dangerous and they are competitive. For me it's important to keep focusing on my game and play one at a time. Quarterfinals of a Grand Slam is never easy, no matter who you play.
"I don't consider myself a favorite because I don't consider anybody a favorite. I just go out there and play my best, because anybody on any given day - we've seen that happen the last couple days - can bring their best game. You have to stay alert. It doesn't matter that you're No.2 or whatever.
"The way I approach the matches, I have to be ready 100% for every player."