It was the first time the two players had faced each other in a tournament, reports Efe news.
Local favourite Wang dominated the match from the start, drawing cheers from spectators as she racked up her 14th straight win.
On Wednesday, Puig had said that she had a lot of respect for Wang.
“She can do whatever she wants with the ball if you give her the opportunity. She’s definitely going to be a tough test for me, especially her playing at home, she’s going to have the home court advantage,” she said.
Wang, ranked 34 in the world by the Women’s Tennis Association (WTA), continued her terrific recent form and broke Puig twice to rush into a 4-0 lead.
Wang took advantage of her opponent’s unforced errors to win the first set 6-3 and took control of the second early on, as Puig appeared to lose focus, becoming frustrated by her frequent unforced errors.
The loss will be particularly disappointing considering Puig’s impressive elimination of world number two Caroline Wozniacki in the previous round.
Wang moves on to the semi-final, where she will face either Estonia’s Anett Kontaveit or the Czech Republic’s Katerina Siniakova.