The Russian is scheduled to play U.S. Open champion Flavia Pennetta later in the day with the result of that match determining who advances out of the Red Group with Sharapova.
Radwanska had lost her first two matches and few would have given the fifth seed a chance of upsetting the highest-ranked player in the tournament after Serena Williams’ withdrawal, especially when she took to the court with strapping around her right thigh and shoulder.
Her hopes appeared even more remote when the world number two seized control of the contest from the outset, breaking in the first game and threatening to repeat the feat several times as Radwanska struggled to find her range.
The Pole, however, is renowned for her tenacious defence and used her supreme retrieving skills to first level up the contest before forging two set points in the 10th game that Halep repelled with some audacious shot-making into the corners.
Still deadlocked after 12 enthralling games, the opener went to a tiebreak and when the players changed ends with the world number two 5-1 ahead, it appeared Halep would seize the set that would end Radwanska’s interest in the tournament.
Her opponent had other ideas though, and threw herself around the court to reel off six straight points and seal the opener when Halep chipped wide at the end of a thrilling rally that had the crowd on their feet in appreciation.
“That tiebreak was something else and I just managed to make some great points at important moments,” Radwanska said in a courtside interview.
“It’s very nice to hear people say my tennis is entertaining so I hope I can keep hearing people say that over and over again,” she added of the spectacular leaping backhand that forced Halep’s error on set point in the tiebreak.
The loss of the set had a demoralising effect on Halep and the Romanian was soon transformed into a helpless spectator as Radwanska stormed through the second set in 30 minutes, breaking three times as she chalked up her 500th win on the WTA Tour.
Despite the thrilling nature of her victory, Radwanska can only advance if Sharapova defeats Pennetta in straight sets. Any other result will send the Italian through to the last four in her final tournament before she retires.