Sakkari, who defeated defending champion Iga Swiatek in the quarters, could not capitalise on a match point as she missed out on becoming the first Greek woman to reach the final of a tennis major.
World number 33 Krejcikova, a title winner in Strasbourg before this remarkable Roland Garros run, overcame her own inconsistency to edge through 7-5 4-6 9-7 in three hours and 18 minutes.
The 25-year-old will face another maiden major finalist in the form of Anastasia Pavlyuchenkova, who defeated Tamara Zidansek in much more routine fashion earlier.
"I always wanted to play a match like this," Krejcikova said of her semi-final win. "Such a challenging match, both had chances, both playing so well, but only one can win. Even if I'd lost today, I'd have been very proud of myself. Fighting is the most important thing."
Krejcikova certainly did have to battle hard, coming back from two breaks down to clinch an enthralling opening set which would set the tone for what was to follow.
Sakkari responded in fierce fashion, and seemed destined to claim a second-set bagel at 4-0 up, yet Krejcikova had other ideas, and three games later she was a break away from restoring parity.
The break did not come, however, with Sakkari holding to love. The Greek's first set point was wasted with a dreadful forehand effort, but she set up a decider at the third time of asking, leaping across the court in celebration, much to the delight of a partisan crowd.
Krejcikova made her opponent wait with a lengthy stoppage between the sets, and Sakkari's momentum appeared to have been dashed as the Czech held to race into a lead.
But Sakkari's composure returned – she dropped a deft touch shot over the net to hold, before capitalising on Krejcikova's sloppiness to make it 3-1.
Krejcikova dragged herself back again, some sensational, down-the-line backhands frustrating Sakkari, who did nevertheless move to within a game of victory.
Once more, Krejcikova refused to roll over, and a dreadful drop shot handed her a reprieve.
Krejcikova took full advantage but saw three match points go begging as Sakkari took her turn to bounce back from the brink.
Victory looked to have been assured when Sakkari sent a forehand long, only for the chair umpire to incorrectly rule the shot as in, but in a remarkable show of resilience, Krejcikova fittingly hammered a backhand down the line to seal a hard-earned victory.