The 27-year-old will meet either world number one Aryna Sabalenka or Italian Jasmine Paolini, who ousted fourth seed Coco Gauff in the previous round, in Monday's final.
Ostapenko, who stunned five-times Grand Slam champion Iga Swiatek in the last eight to improve her lifetime mark to 6-0 against the Pole, got off to a strong start with a break in the first game.
She was broken straight back but earned another one quickly to go 4-2 up.
Alexandrova, who upset sixth seed Mirra Andreeva and world number three Jessica Pegula at the tournament to take her tally to five top-10 wins during the season, struggled with her opponent's thundering groundstrokes, and especially her forehand.
A finalist in Qatar this year, Ostapenko kept up the pressure and cruised to victory after an early break in the second set.
"I don't know but I feel amazing playing here," Ostapenko said. "So pumped up. Those kinds of matches, winning three sets, gives you confidence," she said.
"I was putting a lot of balls in. I am very happy with myself."
Sabalenka, a three-time losing finalists in Stuttgart between 2021-23, looked to be powering through the first set after taking a 3-0 lead, but Paolini fought back to cut the deficit before losing it 7-5.
The tables were turned in the second with the diminutive Italian punishing a sloppy Sabalenka, who was rushing to finish the points with her trademark power but seeing errors pile up, and earning a 3-0 lead.
Paolini lacked a bit of precision, however, and Sabalenka grabbed her chances to claw her way back to 3-3.
The Belarusian then saw Paolini put a volley into the net, to go 5-4 up before firing a sensational crosscourt forehand winner on her first match point to seal victory.
"She makes me work, work for every point. She is a great player," Sabalenka said. "It is hard to get the win. I was just trying to stay aggressive, to put as much pressure on her."