Pierce, who won the title in 2000, the same year she won the French Open, was too consistent for Washington and eased through to a meeting with Nuria Llagostera Vives of Spain.
"It was a bit of a weird match," Pierce said. "I started really strong and she was maybe feeling the pressure and made a lot of errors. At the end, though, she started playing really well."
Pierce broke her twice in overcast, cool conditions on the way to the opening set.
The 30-year-old Frenchwoman, seeded 15th, then broke twice for a 3-0 lead in the second set to all but settle the tie.
Since the Australian Open Pierce has been beaten only by players ranked inside the top four and the winner of two grand slam titles said she is building well toward the French Open.
"The French is my favourite tournament," she said. "It's definitely my goal of the clay court season, if not of the year and I'm feeling good and really excited."