Barthel rolled past Kiki Bertens 6-3, 6-2 despite losing her serve twice. She did, however, cash in five of her six break-point chances and won more than half (27-26) of the points off Bertens' serve.
Lesia Tsurenko stopped Suarez Navarro 7-5, 6-0. She fought off eight of the 10 break points she faced and had eight double faults in the win. But Tsurenko also took 57 percent of the points when Suarez Navarro served.
Sara Errani, ranked ninth in the world and coming off a win last week at the Italiacom Open, is the top seed for the Swedish Open.