The Brit was within two games of securing a quarter-final place after taking a 4-1 lead in the second set, but the Czech powered her way back to come out on top 4-6 7-6(10) 6-1 in an absorbing contest.
Krejcikova said in her on-court interview: “It was definitely a difficult match.
“It was very down, I don’t really know how I turned it around. I’m just happy to be through and happy that I showed that strength in my head.
“At one point, they (the crowd) started cheering when I was serving and they definitely gave me extra energy. So, thank you guys for coming, waiting here and being here, until quite late.”
The match began in inauspicious fashion for Raducanu after Krejcikova claimed an early break.
But the Brit broke back immediately and then sealed the set 6-4, drawing first blood in the space of 54 minutes.
Momentum ultimately swayed in favour of the Czech following a gruelling second set, which included a further break of serve for both players.
Raducanu would take a double break and consolidate with an emphatic hold to love at 4-1, but Krejcikova somehow pulled off a remarkable recovery to take it into a tie-break.
The 22-year-old squandered the first of her three match points with the score at 5-3, as Krejcikova brought the match back on serve.
Raducanu saw two further opportunities to win the match come and go, following two match points at 7-6 and 9-8.
Krejcikova levelled up the match after the tie-break eventually went in her favour at 12-10, which seemed to knock the stuffing out of the British No.1.
The second set may have been close, but the decider was anything but that, and looked like producing only one winner.
Krejcikova held off two break points to take a hard-fought hold at 2-1, and went on to double break Raducanu at 5-1.
She served for the match with relative ease and wrapped up the contest on her first match point to set up a last-eight clash with Iga Swiatek.
As for Raducanu, it will be a frustrating setback after she elected to miss the Billie Jean King Cup finals in order to improve her WTA ranking.
Meanwhile, her US Open doubles partner Carlos Alcaraz will be taking part in the Laver Cup, which begins on Friday.
Alcaraz will be joined by Holger Rune, Casper Ruud, Alexander Zverev, Jakub Mensik and Flavio Cobolli in Team Europe, which is captained by Yannick Noah, with Tim Henman as vice-captain.
Team World features world No. 4 Taylor Fritz, and also includes Alex de Minaur, Francisco Cerundolo, Alex Michelsen, Joao Fonseca and Reilly Opelka, with Andre Agassi captaining the side.
