The victory, on a day where both players had to battle high temperatures, means Raducanu will overtake Aussie star Alex de Minau's partner Katie Boulter as British No.1 on Monday.
After losing the opening game, Raducanu dropped serve in a long second but managed to break straight back.
The 22-year-old broke again to make it 4-3 courtesy of a scuffed dropped-volley effort by Sakkari, who fought back once more following another double fault by the Briton.
After getting her nose in front again, Raducanu held her serve to take the opening set 6-4.
The 22-year-old was looking to continue her impressive streak over the Greek player on her 30th birthday but Sakkari - who beat Boulter earlier in the competition - took a 4-2 lead in the second set.
Temperatures of up to 36 degrees took their toll as a physio was called onto the court to check on the 2021 US Open winner.
However, the break in play reinvigorated Raducanu - who overcame four-time Grand Slam champion Naomi Osaka on Thursday - and she won five successive games to book her slot in the final four in two hours and 10 minutes.
"I think my confidence has been building since Miami," she told the WTA.
"The amount of work I'm doing behind the scenes, to have that in the locker and banked, you know you've done it, it takes a little pressure off the results."
Raducanu will face either fourth seed Clara Tauson or Anna Kalinskaya for a place in the final.
8°C