Twice winner of the Stuttgart tournament, Swiatek was unable to turn the tide against Ostapenko in their first meeting on her favourite clay surface as she fell in two hours seven minutes on Saturday.
Ostapenko stormed to a 4-0 lead against the reigning and three time Roland Garros champion Swiatek, who failed hold serve until her fourth attempt in a comeback to 5-3, before Ostapenko served out the set at love.
In the second, Swiatek squandered a 3-1 lead as Ostapenko levelled two games later, but the next three games went to the second seed to force a decider.
Ostapenko regrouped and never looked back after taking a quick 3-0 lead. She wrapped up matters in the eighth game on second match point.
In her first Stuttgart semi on Sunday, Ostapenko will face Ekaterina Alexandrova who ousted the third seeded recent Charleston winner Jessica Pegula, 6-0 6-4.
"I could probably win in two sets because second set I started to rush a little bit, but in general, I think I was playing well," Ostapenko said on the WTA website.
"Of course she's a great player, obviously. To play against her is a tough battle. Every time I'm expecting a tough battle."
World No.1 Aryna Sabalenka beat her former doubles partner Elise Mertens 6-4 6-1 in her first match after a first-round bye, a second-round walkover, plus no play at all in Stuttgart on Friday due to the Good Friday holiday.
But Sabalenka, a three-time Stuttgart finalist, dropped serve to trail 4-3 in the first set - and upset with a call in which a ball was ruled out - took a photo of a ball mark with her mobile phone during the changeover.
She then won nine of the remaining 10 games to set up a semi-final date with French Open and Wimbledon finalist Jasmine Paolini, who rallied from 4-2 down in the first set to beat former US Open champion Coco Gauff 6-4 6-3.
"Everyone can makie a mistake," Sabalenka said. "But I believe you can't make these kinds of mistakes. I think you must have the courage to admit to it if you make a mistake. But it is OK now."
