Rybakina arrived for the clash after victories over Amanda Anisimova and Iga Swiatek, but the former Wimbledon champion came under pressure against a fresh Alexandrova, before breaking in the ninth game and then claiming the opening set with a hold.
The Kazakh, who staved off three breakpoints in the first set, cranked up her big serve and heavy hitting early in the second to go 3-1 up and applied the squeeze to close in on another win ahead of the semi-finals.
Another break courtesy of a powerful return of serve left Rybakina one game away, and the 26-year-old eventually wrapped up the victory despite some struggles on her own delivery late in the clash at King Saud University Sports Arena.
Swiatek and Anisimova meet later on Wednesday in a winner-takes-all match to decide who joins Rybakina in the last four as the second-best player from the Serena Williams Group at the end of the round robin stage.
It will be their third meeting this season, with Swiatek having crushed Anisimova 6-0, 6-0 in the Wimbledon final in July to claim her first All England Club title before the American gained revenge in the US Open quarter-finals in September.