"I am truly happy and can not believe what I have achieved, " she said after her win over Caroline Wozniacki yesterday.
"I'm not ashamed to say that she played better", said Bacsinszky.
Bacsinszky fended off one with a swinging serve but Riga's finest made no mistake on the second, sending a forehand whistling into the corner to become the first Latvian player to reach a grand slam final.
She consolidated for 4-1 in the next game.
In a remarkable quirk of fate, both women were playing arguably the biggest match of their careers on their birthday.
Coming into Thursday, Halep led Pliskova 4-1 head-to-head and upped that mark to 5-1 lifetime with the victory. With a win in the finals, Halep will become the new world number one.
But the mistakes returned to haunt her in the final set.
Action is due to continue tomorrow with the men's semi-finals.
The fast conditions have helped the Czech and, after Halep controlled the first set, Pliskova found her range on her big serve and forehand in the second. She proved herself by beating the second seed on Thursday, too.
The powerful Pliskova saved three set points to prolong the first set, but Halep mixed up her game superbly and was a set up when her opponent blasted a forehand wide.
Her win over Pliskova was an interesting contrast of styles, with Halep's angles and movement pitted against Pliskova's serving and booming groundstrokes.
But Ostapenko's fearless approach paid off after a series of breaks to start the decider, the Latvian landing the crucial blow to pull 4-3 ahead before sealing victory in two hours and 25 minutes. "She was more successful".
She held her nerve to serve it out, ending the contest with an unreturnable serve, triggering a big roar from the Romanian flag-waving fans on Court Philippe Chatrier.
"It is nice to be in the final again", Halep said.
The first set seemed to fit the pattern many expected.
One who hits the ball as if she's angry at it.
"When I came here, I didn't expect I would be in the final", said Ostapenko. I won the first set and was very close to making the final and some thoughts were in my mind.
Suddenly, Halep had to defend, something she does with poise and grace, but Pliskova had recovered her forehand and it made all the difference as she cracked a victor to seal the second set.