After dropping the first seven games, Halep slowly found rhythm and at 3-3 in the second set shifted into high gear.
Looking like a completely different player to the one who was so unimpressive in the first set, she stormed through the next eight games to level the match and pull ahead 5-0 in the third before Radwanska could stop the slide, if only for one game as the sixth seed was sent packing.
"At the beginning I could not move my legs. I felt very tired," said Halep, 23, playing her first event since a surprise first round exit at Wimbledon.
"I just kept focused on what I had to do and just tried to keep the ball in the court to make some longer rallies.
"She played an amazing first set I couldn't make anything but I am happy I could fight until the end."
Next up for Halep will be the winner of the quarter-final between 15th seed Sara Errani of Italy and Ukrainian qualifier Lesia Tsurenko.
(Reporting by Steve Keating in Toronto. Editing by Andrew Both)
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