Liudmila Samsonova ousted Paula Badosa on Sunday in a three-set victory that lasted three hours 22 minutes.
That record was exceeded by eight minutes a day later - Cirstea prevailing 4-6 7-6 (9-7) 7-5 in her first-round encounter with 11th seed Haddad Maia.
Another marathon encounter was played out on Monday between Veronika Kudermetova and Anhelina Kalinina, with the latter winning 6-3 5-7 7-5 in just over three hours.
Cirstea, ranked 70th in the world, fended off two match points in the second-set tiebreak and took that momentum into the decider.
Brazil's Haddad Maia has lost four of her five meetings with Cirstea, though had defeated the Romanian in Adelaide in January.
"I fought really hard today. I really think I gave it all," Cirstea said.
"I have nothing left. Sometimes you just have to stay in there. Bia played amazing. You know, tennis is not fair sometimes. You play for three hours and a half, and it's a difference of a point.
"I think this is what tennis is about, where all the work pays off. Sometimes it doesn't matter if it's a first round or a final, the joy is the same."
Cirstea will face Czech Karolina Muchova in the next round after she saw off Bernarda Pera 6-1 6-4.
Australian Open champion Aryna Sabalenka received a bye to round two, where she will face Lauren Davis after the American's victory over Jil Teichmann.
Jelena Ostapenko dispatched Katarina Zavatska 6-1 6-4 with the minimum of fuss, while Victoria Azarenka overcame Anastasia Pavlyuchenkova 6-3 7-5.
Azarenka has won 135 WTA-1000 main-draw matches in straights sets, at least three more than any other player.
Karolina Pliskova defeated Marketa Vondrousova 6-3 6-4, while Elena Rybakina, Ana Bodgan, Aliaksandra Sasnovich and Shelby Rogers were also victorious.
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