Raducanu suffered a listless second-round exit at January’s Australian Open and subsequently split with coach Francisco Roig.
However, she has shown real grit throughout her run in Romania to reach the final.
“I’m so proud of how I competed, how I came back in the third set and how I managed the match,” Raducanu said.
“I don’t think I could have done it without everyone’s support here so thank you so much.”
Raducanu’s father, Ion, is from Bucharest and the exhausted but thrilled player briefly addressed the crowd in Romanian after her victory.
Only home hope Sorana Cirstea now stands between Raducanu and her first piece of silverware in five years.
The 23-year-old failed to serve out the opening set at the first time of asking, allowing Oliynykova to break back before winning the next two games – wrapping it up after a gruelling hour and 15 minutes.
But the top seed’s momentum faltered further in the second set and she was broken three times as Oliynykova forced a decider, where Raducanu was forced to fight back from a break down.
And after missing her first two match points at 5-3, the Briton saved two break-back points and served out the win at the third time of asking.
The victory snapped a six-match losing streak in deciding sets for Raducanu, while it was her first three-set win since she beat Ann Li in the first round of Eastbourne in June.