Kasatkina, the 14th seed, had played beautifully to lead 7-6 3-3 on Sunday when play was called off but any hopes Australian Open champion Wozniacki harboured that her 21-year-old opponent's level would dip on the resumption proved fanciful.
It was all over in a matter of minutes on Court Philippe Chatrier as Kasatkina rattled off the three games she needed to reach her first Grand Slam quarter-final.
Having disposed of one reigning Grand Slam champion, Kasatkina, who has dropped just one set so far, will next face another in U.S. Open winner Sloane Stephens.
Dane Wozniacki's wait to make a real impression on the Parisian competition goes on despite arriving with high hopes and dropping only 11 games in her first three rounds.
She had been unhappy at being made to continue the night before after both players called for a stoppage at 1-1 in the deciding set even though the light appeared adequate.
There were no excuses, though, from the 27-year-old.
"You just try and regroup and come back and get a strong start," she told reporters.
"I honestly didn't think I played badly this morning. She didn't miss one ball, and she was playing very close to the lines. I was trying, but it just wasn't enough today."
BASELINE EXCHANGES
Kasatkina poses a different set of puzzles with her varied game, however, and was quite prepared to engage in long baseline exchanges during Sunday's first instalment, mixing her spins and angles to keep Wozniacki guessing.
The Russian, who won the junior title in 2014, had broken in the first game of the match but served three consecutive double faults in her opening service game as some early nerves took hold, although she shrugged that off with a wry smile.
She soon found her rhythm and broke again immediately.
Both players seemed happier returning, though, and Wozniacki began to make her weight of shot tell as she moved 5-3 ahead, only to lose her grip and get dragged into a tiebreak.
Two long rallies went Kasatkina's way for a 2-0 lead before Wozniacki took the next four points.
Kasatkina got back to 4-4 after winning another cagey exchange with a volley after running Woznaicki ragged.
Wozniacki's patience snapped at 5-6 and she blazed a forehand wide to hand Kasatkina the first set after 69 minutes.
Kasatkina was unshakeable on Monday and outlasted Wozniacki to win a 32-stroke rally to move 5-3 ahead before claiming victory when Wozniacki pulled a return wide.
(Reporting by Martyn Herman; editing by John Stonestreet and Christian Radnedge)
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