Putting pressure on Pliskova's serve, Cirstea won six of seven break points and hit 16 winners to score her first win over a top five player in over four years.
"I didn't think about her ranking, I just focused on my game," Cirstea told a news conference after third-round clash.
"I've been playing well lately, it's just that probably results didn't come as quick as I hoped. But I was working well lately... and I always say that hard work will pay off in the end."
Two-times Wimbledon champion Petra Kvitova produced 38 winners as she trounced another former world number one, Caroline Wozniacki, 6-1 6-4. Wozniacki failed to convert four break points as Kvitova won in an hour and 13 minutes.
Earlier, French Open champion Jelena Ostapenko progressed when China number one Peng Shuai retired with a knee injury while trailing 3-0.
"It's not the result I wanted to have," Ostapenko told a news conference after the match. "Of course I feel bad for Shuai, and hopefully she can recover and will be fine."
Ostapenko, who next plays Cirstea, added: "Maybe for me, it was a little advantage that I didn't have to play the full match, as I was playing a lot of matches in the last couple of weeks, so I can rest a little bit more."
Caroline Garcia kept alive her hopes of pipping Johanna Konta to the final spot in the season-ending WTA Finals when she defeated fellow Frenchwoman Alize Cornet 6-2 6-1.
(Reporting by Shrivathsa Sridhar in Bengaluru; editing by John Stonestreet)
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