The No.6-seeded Stephens had her chances in the first set - she led 4-2, served for it at 5-4, and had all the momentum in the tie-break as she battled back from 1-5 to tie it up at 6-all; but every time the No.4-seeded Wozniacki stepped it up and she eventually won the match in straight sets, 76(6) 62.
"I was really, really pleased about my game tonight," Wozniacki said afterwards. "I definitely went out there with aggression and felt like I was playing really well, taking the ball early - I also thought that Sloane played really well tonight, as well, so I was obviously really pleased about the win tonight."
Wozniacki was asked about stepping it up and breaking back while Stephens served for the first set.
"I was playing great tennis, I just needed to step in even more for the returns," Wozniacki said. "I also thought if I lost the set, it was too good from her - but I still had another set to try to make it up.
"I just had to keep doing what I was doing, because I was feeling really good out there."
Stephens was asked about what makes Wozniacki so tough to play. "She gets a lot of balls back. She's a really great competitor. She plays her strengths really, really well, and she knows what she's doing. She's a smart player. She's been No.1 in the world. She really knows what it takes to be up there.
"Obviously she's worked really hard on her game and knowing what she needs to do best - that's what it takes to be good. She's a consistent Top 10 player. So I think she has a pretty solid game."
Wozniacki responded to the compliments. "Not everyone is gifted with a lot of talent - obviously you have to have some talent to reach the top - but the hard work, the work ethics, the competitiveness, I think that's what brings you all the way to the top. You can reach a certain level with talent and with hard work, but you really need that competitive spirit to make it all the way up there in this sport."
Does Wozniacki think Stephens has that? "Yeah, for sure," she said. "She has very powerful strokes. She has a very good serve. I was actually surprised how well she was running, as well. She ran a lot of balls down. I can definitely see a very bright future for her - she's already had a great career."
"I played really well in the first set and she wasn't playing so well - she made a lot of mistakes first set," Halep said after the match. "But at 1-all in the second set it rained and the match was suspended. I was a little bit nervous after that and it took me a little bit of time to get back into the match afterwards.
"But I managed to come back from 4-2 down in the second set and did well from there, so I'm happy."
Halep should be happy, as she has now won 27 of her last 32 WTA main draw matches. She has also made it through to the ninth WTA semifinal of her career - and her first WTA semifinal on hardcourts.
"I've been playing more aggressively and moving better this year - I'm feeling very, very good at the moment," the Romanian said. "I'm a bit tired right now, but tomorrow I'm just going to try my best."