Ormaechea proved to be a difficult opponent for the eighth seed in the first set as both players traded breaks of serve in the opener.
However, Kvitova proved to have enough quality to find a crucial second break on her way to taking the lead with a 6-3 success.
Holding serve continued to be a problem for both competitors, with three breaks occurring as Kvitova moved 4-3 ahead in the second set.
However, Ormaechea fought back admirably to break Kvitova and ensure she pulled level to halt her rival's progress.
The Argentine failed to take full advantage of a second chance as she once again gifted the lead to Kvitova, who held her nerve to win the set and book her spot in the third round.