With the British number one looking to seal victory she stuttered allowing Martic to begin an impressive fightback.
She will play Kaia Kanepi of Estonia in the last eight with the other quarterfinal between Bojana Jovanovski and Petra Martic.
The women's 2011 winner Sam Stosur was drawn against Croatia's Petra Martic, with top seed Victoria Azarenka playing world No. 74 Alexandra Panova.
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The Nottingham champion and Eastbourne quarter-finalist was then broken twice more to leave Martic only needing to win her next three service games.
Baltacha had enjoyed her first-ever main draw win in the tournament when she beat Petra Martic in round one, but Kvitova proved just too strong.
The 26-year-old had been tipped to reach the second round with Martic ranked 15 places below her and having only been at Wimbledon once before.
The 27-year-old recovered from a 2-6 7-5 6-3 first round defeat by Petra Martic at the All England Club to end the year as world number 55.
And it looked as though the Briton would be progressing to the next round when she coolly broke Martic for a third time to lead 3-2 in the second set.
The world No. 19 was leading 6-1 4-1 when Suarez Navarro retired due to a back injury and will face either Petra Martic, from Croatia, or the Czech Republic's Petra Cetkovska in round three.
China's Li Na, the 2011 French Open champion, quickly wrapped up a 6-3 6-1 win over Ksenia Pervak from Kazakhstan while Sabine Lisicki, the German No. 15 seed, recorded a 6-4 6-2 victory over Petra Martic.
Hungary's Agnes Szavay walked into the second round when Olga Govortsova of Belarus retired hurt while trailing 6-3 1-0, and will face third seed Yanina Wickmayer in the second round if the Belgian beats Croatian wildcard Petra Martic.
Having crashed out at Wimbledon in June the Scot did not find her best form until the US Open in August, when she won her first ever main draw match at Flushing Meadows by beating, ironically, Martic.
Twelfth seed Agnieszka Radwanska enjoyed a relatively comfortable passage into the third round with a 6-3 6-4 win over Croatia's Petra Martic, and the Pole will play Simona Halep after the Romanian beat Russia's 24th seed Alisa Kleybanova 6-4 7-6 (7-2).
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