Cirstea not only dropped the first set but had to fight back from 5-3 down in the third set - and a match point - to squeak past Russian qualifier Alla Kudryavtseva in a three set nail-biter, 26 61 75.
"First of all, I'm happy with the result," Cirstea said after the match. "I got in at 2 o'clock last night and only had six hours of sleep. Also, I was playing indoors in Fed Cup last week - here it's outdoors, a different surface, different balls, everything was different. I really had to adjust out there.
"In the first set I was still trying to find my game a little bit. I adjusted well in the second set but in the third set I knew I just had to keep fighting. She had a match point. Sometimes you lose from match point and sometimes you win, but you just have to keep trying and fighting your hardest."
Cirstea's fellow Romanian Monica Niculescu, who came from the same Fed Cup tie, had a simpler 61 60 win over Omani wildcard Fatma Al Nabhani. "Even though I went to bed at 2 o'clock and was coming from the indoor conditions of Budapest to here, I felt great," she said. "I love this tournament - the surface, the conditions - I didn't hit outdoors for two weeks, but I'm really happy how I did today."
Some other late arrivals - Czech Fed Cup heroines Lucie Safarova and Klara Zakopalova, who wrapped up their victory against Spain on Monday - were both winners too. Zakopalova beat Elina Svitolina, 62 64, while Safarova battled to the end to beat No.16 seed Kirsten Flipkens, 57 64 64.
"I was very tired," Zakopalova said. "I slept just one hour at the hotel, so I didn't expect I could win the match, but I was just fighting every point and I won. I don't know how I did it but I'm very happy!"
"Klara and I flew overnight from Spain, so we didn't sleep at all," Safarova commeted. "We got here at about 11 o'clock and I went to sleep for about half an hour, and then I went straight on court.
"I'm really exhausted. But I'm happy I was able to win today!"
The four biggest names in action had mixed results. No.9 seed Ana Ivanovic and No.12 seed Sam Stosur both moved through their first round matches smoothly, but No.10 seed Dominika Cibulkova had to retire at 5-all in the first set against Russian wildcard Alisa Kleybanova due to illness and No.15 seed Eugenie Bouchard was bounced by Bethanie Mattek-Sands, 75 61. Bouchard led 5-3 in the first set and had double set point up 5-4 but Mattek-Sands won 10 of the last 11 games of the match.