The Spanish world number 70 had a fraught buildup to the tournament, testing positive to the novel coronavirus while in quarantine last month.
Her infection saw her transferred to a separate “health hotel” where COVID-19 cases are isolated, and the clock on her mandatory period of isolation was restarted.
Badosa complained bitterly about the experience, saying it was “far and away the worst” of her career.
Unable to compete in any of the leadup events, Badosa was short of match fitness when confronting Samsonova on a warm afternoon and was dragged into a dogfight by the world number 130.
She battled into a position to serve for the match at 5-4 in the deciding set but ended up double-faulting on break point.
Fatigue appeared to take it toll as she served to stay in the match, and Samsonova took full advantage, running Badosa ragged until the Spaniard sprayed a shot wide on match point.
Samsonova advances to a second round match against last year’s finalist Garbine Muguruza. Reporting by Ian Ransom; Editing by Peter Rutherford