Errani, who clinched the seventh WTA title of her career in Acapulco last month, broke her opponent's serve twice in the opening set and three times in the second to seal the win in one hour 21 minutes on a sunny day at Indian Wells.
The 25-year-old Italian, known for her doubles prowess, will next face either Russian Svetlana Kuznetsova or ninth seed Marion Bartoli of France, who were scheduled to play later on Sunday.
"The score was 6-3 6-1 in the end, but for sure it wasn't that easy a match," Errani told reporters after improving her win-loss record for the year to 20-7.
"Many of the points were very long and she's a very strong player. It was a much tougher match than the score."
Errani, who reached her first grand slam singles final at last year's French Open, was delighted to become the first WTA player this season to post 20 match wins.
"For sure I'm very happy about that," Errani said with a smile. "I like competition much better than practice, so I play a lot of tournaments and a lot of matches - I really enjoy it.
"For the moment I'm doing well. Right now I'm very happy to still be in this tournament and I hope to keep going."
Czech Klara Zakopalova also advanced to the fourth round on Sunday, beating Slovakia's Dominika Cibulkova 6-4 7-5.
Later in the day, Russian world number three Maria Sharapova was scheduled to play Spaniard Carla Suarez Navarro, while third seed Agnieszka Radwanska of Poland meets Romania's Sorana Cirstea.