Each had also reached the quarter-finals without dropping a set, and had surrendered only 23 games in four matches.
Ostapenko was able to pull one of the breaks back, but was soon in trouble again, staring down four break points.
The pattern continued in the second set as 2017 French Open champion Ostapenko's unforced errors - which totaled 35 by the end of the match - gave Kerber two more breaks of serve for a 5-1 lead.
A delightful drop shot saw the Latvian bring the set back on serve, however, before a backhand victor down the line delivered a break that left her to successfully serve for a 1-0 lead.
"I was down in the first set but I kept fighting".
The 21 year old won 7-5,6-4 in straight sets on court one. She's come back from a set down 38 times in the majors. By now she was screaming curses in Russian, cocking her fingers and pretending to shoot herself in the head.
The Slovakian's patience was tested again when a backhand she struck onto the baseline was called out. She lost her very first service game through two double faults, one on break point, which meant Kerber was 3-0 up after just 10 minutes.
Kasatkina made an encouraging start, putting away a forehand victor to earn a break point in the first game, but Kerber escaped with a battling hold and the 14th seed gifted her a 2-0 lead after double-faulting twice in a nervy first service game.
Despite getting a first-set runaround from the pocket-sized Italian, who was enjoying her best run at a grand slam, Williams stayed unusually calm, though insists it was a one-off. "I'm so excited", Kerber said. But then slowly I got used to the rhythm, started to feel my game. "Sometimes. I'm also complaining because I think it was a wrong call".
"I feel good, I feel like I did better today, I had to", she told BBC Sport. "It was (a) really bad decision from the supervisor and from the umpire".
Jelena Ostapenko said that she was playing without any pressure as there was no added burden of defending the title in Paris, as she was knocked out in the first round itself in the month of June. Finally, it's gone. Now it's another tournament, another great opportunity for me. "I was just trying to push myself until the limits actually". I think I'm serving very well this tournament.
Cibulkova has won both of their previous matchups, but she isn't going to be focused on anything but what she has to do to reach her first Wimbledon semifinal: "I played her couple of times".
Does she have an explanation as to why all these top-10 players fell early? Just going to prepare well for the match. "This is all I'm focussing on".
Dominika Cibulkova couldn't match the power of her opponent at the Wimbledon Championships on Tuesday. This appeared to boost Kerber, 30, and she soon found her range to move 4-1 ahead in the opener. But unlike in the quarterfinals, when she needed seven match points to win, this time it required only two, with the match ending - fittingly enough - on a forehand by Ostapenko that sailed wide.