After tucking away a routine first set, the No.14-seeded Stephens battled back from 5-3 down in the second set and regrouped after missing out on a match point at 6-5, closing it out in the breaker.
"It was definitely tough. She upped her game a lot in the second set," Stephens said. "Sometimes it's going to be a little up and down, but I thought I stayed pretty solid and managed to get through it."
"I just needed to play a lot more," Stephens said. "I needed to play more sets, just needed to get back into it. I was still in vacation mode and needed to get back to reality. It's business time again.
"It's definitely good to get a win here. I'd never played here before, and it's definitely a totally new atmosphere for me, totally new conditions. But I'm definitely happy to get a win out there tonight."
And Stephens' vacation mode, did it actually spill over from a vacation? "I was in Hawaii," she said. "No tennis. My ab was still acting up. I couldn't even serve - before Wimbledon I didn't serve at all. I went into Wimbledon serving one day. Then obviously it was acting up during Wimbledon, so afterwards I obviously needed to take a break and couldn't really do anything. So I ended up going to Hawaii."
"She's a great player and she played a good first set," Vinci said. "I was 3-0 down in the third set. It was difficult. There was a lot of wind, especially on one side. In the third I tried to play aggressive and also put a lot of balls in the court because sometimes she plays an unbelievable game, then sometimes not so good - she has a lot of ups and downs. The most important thing is I won the match, though."