Despite three straight double faults in her opening service game, it was Kasatkina who chalked up an early 3-1 lead, illustrating her variety and raw power on Court Philippe-Chatrier.
Australian Open champion Wozniacki, who only surrendered 11 games en route to the last 16, began drilling shots from corner to corner and applying pressure with relentless retrieval, clinching four successive games to surge to the brink of the opening set.
However, Kasatkina’s rocket-like forehand was keeping Wozniacki guessing, with one particular piercing inside-out effort drawing gasps from the large, captivated crowd.
Locked at 5-5, Wozniacki managed to hold from 0-40, and a tie-break ensued.
The second seed dictated play to open up a 4-2 lead, but Kasatkina prevailed in two astonishing rallies that involved chasing drop shots, reaction volleys and looping lobs.
On the hour mark Wozniacki flashed a brace of forehands wide of the mark and the 21-year-old headed back to the chair with the ascendancy.
With the light fading, both players debated calling it a night, before a raucous crescendo of applause from the crowd urged them to continue. Sadly for those in the stands, the match was suspended shortly after and will have to be continued on Monday.
The eventual winner’s reward is a quarter-final clash with US Open champion Sloane Stephens, who stormed past 25th seed Anett Kontaveit 6-2 6-0.