Errani, seeded No. 1 at the event, ousted Julia Cohen 6-0, 6-1, winning two-thirds of the points in the match. Errani landed a sterling 82 percent of her first serves and won three-quarters of the points in those situations. She faced two break points, saving both.
She also won more than 60 percent of the points off Cohen's serve while finishing with five breaks.
Monday two other main-draw matches went the full three sets.
Seventh-seeded Silvia Soler-Espinosa topped Mathilde Johansson 6-4, 1-6, 7-5. Johansson, due to the lopsided second set, actually won more points than Soler-Espinosa but Soler-Espinosa had the advantage in the first and third sets.
Corinna Dentoni defeated Caroline Garcia 5-7, 7-4, 6-4 in a 2 1/2-hour battle. Dentoni won despite having to deal with 13 break-point opportunities for Garcia. She lost only two of those points.