Williams, the number one seed, was simply too strong for Barthel as she recorded a 6-4 6-1 win.
However Williams was full of praise of the German after the match.
"I didn't know much about her, though, but I knew her name," said Williams.
"She's an interesting player. She seemed so light and so smooth so you don't expect a ball to come that hard.
"That was a little surprising but once I got used to it, it was a little better."
Williams will now take on Simona Halep, who followed up her win against Marion Bartoli with a three-set win over 11th seed Sam Stosur.
Halep eventually came out on top against the former US Open champion 6-4 4-6 6-2.
Caroline Wozniacki is also through to the quarter-final after she recovered from a slow start to topple Petra Kvitova.
Wozniacki, the 10th seed, lost the opening set but she held her nerve to beat the seventh-ranked Kvitova 3-6 6-2 6-3.
Fourth seed Agnieszka Radwanska won her quarter-final match Elena Vesnina 6-0 6-2 but then pulled out of the tournament following the death of her grandfather.
"The funeral is going to be Saturday and I need to be there," she said.
"I am disappointed to not continue with the tournament, especially because of my form so far this week. But I need to be go home and be with my family."