The 36-year-old Romanian, who will retire later this year, beat a world No.1 for the first time in her career on Saturday, but world No.1 Sabalenka was left with an injury concern with the French Open looming.
"I'm very happy with the win. I thought I played really well today. I'm working really really hard. It's nice to have this result as pay-off," Cirstea said.
Four-time grand slam winner Sabalenka struggled with lower back pain as the match progressed, and took a medical timeout when Cirstea was leading the third set 4-3.
"Felt like my body was limiting me from performing on the highest level," Sabalenka said afterwards.
"She stepped in and played incredible tennis. Didn't really give me much opportunities ... but I guess we never lose, we only learn, so it's okay.
"Probably it's my lower back, connected to the hip, which is limiting me from the full rotation. We are going to have some days off, spend it on recovery. That's the plan for now."
Cirstea won the next game after the time-out but Sabalenka fought back to make it 5-5, only for the Romanian to break again to be able to serve for the match.
Sabalenka, struggling with her backhand returns, plopped one into the net and sent two shots over the baseline as Cirstea clinched victory.
It was her second win over the Belarusian in four meetings, having also prevailed in Miami in 2023, the first time they played each other.
"Maybe if I win the tournament, I promise I will think about not retiring," joked Cirstea, who owns four singles WTA titles.
Defending champion Jasmine Paolini also got knocked out, the Italian wasting three match points in a 4-6 7-6 (7-5) 6-3 loss to Elise Mertens in the third round.
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