Unseeded for the WTA International hard-court event, Bertens ousted her opponent in just over two hours, to become the first woman to reach the next round.
The Dutchwoman sent down five aces to Schmiedlova's none, and won 70 per cent of points on her first serve, compared with just 59 per cent for the eighth seed Slovakian.
Bertens made a fine start in the opening set, breaking Schmiedlova twice on her way to a 5-1 lead, before moving ahead by taking advantage of her first available set point.
The second set was a much more closely fought affair, with Bertens forced to save six set points at 6-5 down, before eventually holding to force a tie-break.
Despite wasting a match point in the breaker, Bertens made no mistake at the second time of asking as she sealed her progress to the last 16.
In the other first-round match to take place on Monday, USA's Grace Min overcame Julia Glushko 6-4 6-2 to set up a possible second-round clash with top seed Sabine Lisicki.
Both players showed weaknesses on their own serve early on, as the opening six games saw four breaks, two for each player.
World number 119 Min took the initiative in game 10, however, breaking Glushka to seal the first set after 48 minutes.
Min then assumed complete control in the second set as she raced into a 5-1 lead, and even a brief interruption for rain could not halt her progress as she cruised into the next round.