As the fourth seed for the WTA International hard-court event, the Czech came into the clash as the favourite to progress and she lived up to that billing in securing a straight-sets victory.
Zahlavova-Strycova broke her opponent in the very first game of the match, and was able to hold her serve throughout the remainder of the opening set to take the lead.
The world number 31 repeated her strong start in the second and, after seeing three match points come and go in game nine, eventually wrapped up the win with a deft forehand volley at the net.
Monica Niculescu, who reached the final in 2011 and 2012 only to fall to Victoria Azarenka and Venus Williams respectively, got her quest for a third showpiece appearance in four years off to a satisfactory start with a 6-2 6-2 win over Antonia Lottner.
The eighth seed made short work of her opponent, ranked 468 in the world, breaking the German on five occasions to wrap up victory in just one hour's play.
Niculescu will now take on Mona Barthel in the second round, after Barthel's 6-3 6-4 triumph over Mandy Minella.
Sixth seed Roberta Vinci had a similarly smooth ride against Tereza Smitkova, defeating the Czech 6-1 6-3, a triumph which included six breaks of serve.
Karin Knapp was forced to retire when 3-2 up on Patricia Mayr-Achleitner in the first set while elsewhere, Jana Cepelova dismissed Maria-Teresa Torro-Flor 6-3 6-0.