The Dutchwoman’s reward for a hard-fought 4-6 6-2 6-3 victory after more than two hours on court is a last-four encounter against seventh seed Caroline Garcia, who breezed past Carla Suarez-Navarro 6-2 6-3.
Sharapova had overcome Kristina Mladenovic to reach the quarters, and carried that form with her into the opening set, taking it 6-4 with a crucial break in the 10th game.
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However, the Russian’s serve capitulated in the second set as Bertens, who beat Caroline Wozniacki in the last 16, broke three times to level the match.
Service problems continued for world No 52 Sharapova in the decider as she fell 5-1 behind.
Bertens could not serve out for the match at 5-2 as Sharapova got one break back, but the world No 20 broke her opponent once more to take the final set 6-3.
Elsewhere, Karolina Pliskova proved too strong for world No 1 and two-time defending champion Simona Halep, prevaling 6-4 6-3 after 70 minutes on court.
Pliskova broke the Halep serve four times en route to victory, and she will now play either Daria Kasatkina or Petra Kvitova for a place in the final.
Halep, who has won the tournament for the last two years, had looked imperious on her way to the last eight, dropping only nine games in three matches including Wednesday's win against Pliskova's twin sister Kristyna.
But her winning streak in the Spanish capital ended at 15 matches as her 26-year-old opponent continued her impressive form on the red clay having won the Stuttgart title last month.
It was sixth seed Pliskova's first claycourt victory over Halep and it was the kind of authoritative performance that will turn a few heads as the French Open looms later this month.
Pliskova broke for a 4-3 lead in the opening set and although Halep saved two set points serving at 3-5 Pliskova closed out the opener with a love hold.
Romanian Halep's error-count was surprisingly high and she found herself under pressure early in the second set as Pliskova pounced to break in the third game.
Halep could make little impression on Pliskova's powerful serving and she buckled at 3-5, dropping serve again to bow out.
Additional reporting from Reuters
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