Kvitova, who lost at this year’s Wimbledon quarterfinals against Serena Williams, was serving for the match at 6-4 5-4, just before Bogdarenko staged a superb comeback and forced a decider.
However, the Czech managed to regroup in the third set, taking her opponent’s serve twice to book a place in the second round, where she will meet Chinese Peng Shuai.
Former world no.1 Caroline Wozniacki also needed three sets to overcome Britain’s Anne Keothavong as she came back from a set down to win 4-6 6-3 6-2.
Keothavong enjoyed the massive support of the Wimbledon crowd and they certainly motivated her to come up with her best. Unfortunately for her, Wozniacki dominated the last two sets, setting up a second round encounter against the Belgian Yanina Wickmayer.
Also through to the next round are Italy’s Francesca Schiavone, who eliminated Klara Zakopalova of Czech Republic 6-3 3-6 6-4 and Slovakian Daniela Hantuchova after ousting Chinese Li Na 6-2 3-6 6-3.