The No.23-seeded Hampton was the first to win, beating Kristina Mladenovic in a one-hour, 49-minute contest, 75 64. Mladenovic actually hit more winners in the match - 27 to 23 - but Hampton was by far the more consistent of the two, keeping her unforced errors down to 33 while Mladenovic had 46.
Over on Arthur Ashe Stadium, the No.15-seeded Stephens didn't get on court until almost midnight but it didn't really seem to matter, as she dropped a 58-minute, 61 61 drubbing onto Urszula Radwanska.
Stephens had some very impressive numbers for the match: 24 winners to just 11 unforced errors.
"Literally every 10 minutes they kept saying, 'If Murray plays long, we'll move you. If it rains, we won't.' I'm like, 'Oh my God, it's horrible.' I never started that late. It was a long experience," Stephens said.
"But I played well. Maybe I should do that more often."
Stephens had actually lost the pair's only previous meeting, at Indian Wells earlier this year. But this was a much different Stephens - calm, confident, collected and perhaps most of all, aggressive.
"I was kind of nervous playing her. She plays a lot like her sister. They're tough to play. I lost to her at the beginning of the year. Completely different mindset now. I knew I had to come out and be aggressive and make a lot of balls. I just thought to myself, 'I'm going to go out and do my best.'
"I came out with a really good attitude, and I think it showed," Stephens added. "I think every point was the only thing on my mind. That's what happens when you really, really, really want to win."
And Stephens' thoughts on playing on Ashe? "I was like, 'Why do they want to see me second match after Murray?' I was like, 'Oh no.' I thought there were going to be like two people out there. But there was a pretty good crowd out for so late. Winning my first match on Ashe is a really good feeling.
"Hopefully more to come."
Stephens leads Hampton in their head-to-head series, 2-1, and won their only hardcourt meeting.
"It's always tough playing another American, obviously," Stephens said. "Jamie is a good friend. Obviously it will be a good match. Playing at the US Open, it's a pretty big deal. I'm excited.
"Every person plays a different game, but I think Jamie is like me. We all have our weaknesses and our strengths. I'm going to play my game, she'll play hers. I think it'll be pretty straightforward."