Four-time Grand Slam champion Osaka twice battled back from a break down in the second set to force a decisive third but world number 17 Samsonova eventually ground out the victory.
Japanese player Osaka returned to tennis in January after a long break and earned her first victory on clay for two years on Wednesday against Greet Minnen.
However Russian 15th seed Samsonova, whom Osaka beat at Indian Wells in March, was able to end a four-match losing streak with her victory in two hours 22 minutes in the Spanish capital.
Hard-court expert Osaka is not overly fond of clay and has not won back-to-back matches on the surface since 2019.
Samsonova raced into a 4-0 first-set lead, breaking in the first and third games as Osaka struggled.
After recovering an early break Osaka was broke again in the fifth game and Samsonova took a 4-2 lead. However, Osaka battled back and won the next four games to take the set.
In the decider, the players exchanged breaks before Osaka eventually blinked in the 11th game, with Samsonova wrapping up victory on serve. She will face Madison Keys in the next round.
Later Thursday, world number one and last year's runner-up in Madrid, Iga Swiatek, faces China's Wang Xiyu.
