Andy Murray lost to Aslan Karatsev in the final of the Sydney Tennis Classic 6-3, 6-2 as his two-year wait for an ATP title goes on.
Kasatkina will next take on No.5 seed Paula Badosa, who overcame Belinda Bencic 7-6, 3-6, 6-3 in 2 hours and 35 minutes.
For the first time in five meetings, Jabeur managed to get one past the two-time Wimbledon champion.
The physically-demanding encounter lasted a staggering three hours and 15 minutes on Ken Rosewall Arena.
Rybakina is fresh from reaching her eighth career final in Adelaide last week before falling to Ashleigh Barty in the title match.
This comes after the former World No.1 lost to Facundo Bagnis in his first match of the season last week in Melbourne.
Petra Kvitova had survived two match points in the final set to overcome Arantxa Rus, 3-6, 7-6, 7-5.