The 25-year-old made an early breakthrough on her Spanish opponent's serve to go a break up in the set.
She then proceeded to hold her remaining service games to eventually take the opening set 6-3.
Blanco responded positively against the current world number 10 in the second set though. Both players had chances to claim a break of serve, but neither was able to take advantage of the opportunities presented to them.
As a result, the set headed into a tie-break, which was also evenly contested until Blanco claimed a break that allowed her to win 8-6 and force a decider.
Despite the setback, Errani gained control of the third set from the very first game thanks to a number of forehand winners. The Italian eventually broke for a third time to secure a 6-1 triumph and her passage into the next round, where she will come up against Russia's Vera Dushevina.