The 18-year-old came into this week’s event ranked at a career-high number 74 in the world, and the WTA's youngest top-100 player produced an inspired display to seal her place in the tournament showpiece and continue her hugely encouraging run.
Durie was the last British woman to contest a main tour singles final back in Newport, USA in 1990. The last British woman to win a WTA singles title was Sara Gomer in July 1988 in Aptos, California.
It was another impressive performance from Robson, who dumped out China's Peng Shuai in three sets in the previous round. but only needed two to get rid of Cirstea in just under 90 minutes.
Robson never allowed Cirstea to settle, comprehensively outplaying the world number 30 from the back of the court to move into a 5-1 lead, although she wobbled while serving for the set and needed to break back to claim it.
The London-based teenager reached the fourth round at the US Open - where she beat former champion Kim Clijsters and former French Open champion Li Na - after picking up a silver medal at the London Olympics alongside Andy Murray in the mixed doubles, and she was utterly relentless as she stormed 3-0 up at the start of the second set.
A change in racquet for Cirstea allowed her to regain her composure, saving several break points in one epic game and breaking back at 5-1 to Robson, who again failed to serve for the match at the first time of asking.
But the Briton unleashed some of her trademark power returns to break again and claim another top-30 scalp in a superb run which started at Palermo in July, where she reached her first Tour semi-final.
Cirstea, who was playing in her fourth semi-final of the year after Pattaya City, Barcelona and Stanford, was looking to make her first final since her lone title at Tashkent in 2008, but she could not match Robson’s intensity.
The Romanian put in half a dozen aces, but she made too many unforced errors, while Robson's shot-making was as accurate as her serving was inconsistent, her six double faults pointing to a slight weakness in her game - albeit one caused by an adventurous style.
Despite coming into this week on a four-match WTA losing streak, Hsieh has dropped just 14 games in her four previous matches, and she will now take on Robson in an unlikely match-up in Saturday morning's final.
They have contrasting styles, with Hsieh more experienced and mobile but Robson the bigger shot-maker, but both are full of confidence in what should be an entertaining spectacle.
Robson is guaranteed a top-60 place now, with a win pushing her closer to the top 50 in what has been a remarkable season for the youngster.