The Japanese sixth seed won 6-2, 6-2 in just 59 minutes to reach the final four of the grass-court tournament just days out from the start of Wimbledon.
Osaka, the world number 15, is one win away from a first grass-court final of her career.
"Obviously I can't say that I've had much experience on grass, but I feel really good right now," Osaka said, adding that coach Tomas Wiktorowski, who started working with her last July, "is helping me understand grass a lot more, so I feel pretty comfortable at this point."
Osaka was broken early in the opening set but swiftly struck back against the unseeded Russian.
Osaka won eight straight games - a run which included 15 points in a row - as she took the opening set and ran out to a 3-0 lead in the second.
The 19th-ranked Alexandrova rallied to win her next two service games, but Osaka closed out the match in just under an hour.
Osaka will play Chinese world number 52 Wang Xinyu, who reached the final four when eighth-ranked Ukranian Elina Svitolina pulled out citing exhaustion on Wednesday.
Romania's Elena-Gabriel Ruse also made the final four after a straight-sets victory over American Emma Navarro. Ruse won 6-4, 6-2 in one hour and 15 minutes.
Later on Thursday, fourth seed Karolina Muchova takes on Dane Clara Tauson.