The Italian was the only seed in action on the opening day of the WTA Premier clay-court event, and successfully closed out the match 7-5 6-1 after battling hard to win the opening set.
Despite breaking her German opponent's serve early on, Errani was pegged back in the sixth game as the set looked to be heading for a tie-breaker.
But Errani claimed the 11th to leave herself serving for the set, and eventually moved into the lead after squandering one set point.
The 10th seed then cruised to victory in the second set to book a meeting with either Elena Vesnina or compatriot Francesca Schiavone in the next round.
Estonia's Kaia Kanepi let a one-set lead slip as she fell to a 6-7 (7-9) 6-1 6-2 defeat at the hands of Alison Riske - ranked 23 places below her opponent.
Garbine Muguruza emerged as 6-7 (4-7) 6-3 7-6 (7-2) victor in an all-Spanish clash with Silvia Soler Espinosa, while the United States' Christina McHale beat compatriot Lauren Davis 7-6 (7-2) 6-3 to set up a potential second-round meeting with Maria Sharapova.
Magdalena Rybarikova triumphed 6-2 7-5 over Annika Beck of Germany, and Bojana Jovanovski could meet fellow Serbian Ana Ivanovic in the next round after beating Karin Knapp 6-1 6-1.
In the day's remaining first-round encounter, wildcard Lara Arruabarrena came away with a 6-3 6-4 win against Tsvetana Pironkova.