Cirstea, who has yet to drop a set in Miami and is the last unseeded player in the draw, delivered a stunning performance while taking advantage of some untimely double faults to become only the third person to beat Sabalenka this year.
With the win, Cirstea reached her second WTA 1000 semi-final nearly 10 years after reaching her first.
"I am a bit speechless," said world number 74 Cirstea. "I came out knowing that it was going to be a really tough match.
"Aryna hits so hard, so I knew I had to hold my ground and I am very, very happy with my performance today and it's a bit unexpected to be honest."
When serving for the match, Cirstea fell behind 0-30 and then held steady while saving two break points before finally sealing the win when Sabalenka sent a forehand return long.
Cirstea broke to open the match but Sabalenka dropped just three points across her next three service games before breaking the Romanian to draw level at 4-4.
But Cirstea, who arrived in Miami fresh off a run to the Indian Wells quarter-final, held firm against Sabalenka's power and broke right back before sealing the first set in emphatic fashion with an ace.
The Romanian broke to start the second set when Sabalenka double-faulted at 30-40 and then held to love for a 2-0 lead but the Belarusian briefly turned up the heat and looked to have found her way before letting it slip.
Sabalenka, a runner-up at Indian Wells, squandered a break point chance while leading 3-2 and then double-faulted while facing a break point in the next game as Cirstea went ahead 4-3 and never looked back.
Cirstea will face either Czech 15th seed Petra Kvitova or 18th-seeded Russian Ekaterina Alexandrova in the semis.
On the men's side, a two-hour mid-match rain delay could not cool off sizzling Jannik Sinner, who crushed unseeded Finn Emil Ruusuvuori 6-3 6-1 in their one-sided quarter-final.
The 10th-seeded Italian ripped a backhand return winner to capture the first set and rolled from there to improve to a career 5-0 against Ruusuvuori.
"We both played well today but I won the important points," said Sinner.
"It's never easy when you are up and you get interrupted, but I came back and played well."
Rain washed out Wednesday's remaining matches, including a first meeting between world number one and defending champion Carlos Alcaraz and American Taylor Fritz. That match will be held during the evening session on Thursday, weather permitting.
