Roma's Cengiz Under scored in the 41st minute at the Metalist Stadium in Kharkiv, but goals from Facundo Ferreyra (52) and Fred (71) secured a 2-1 victory for the Ukrainian club, Ukrinform reports.
In the current season of the Champions League, Shakhtar won all three home matches in Group G. Paulo Fonseca's side defeated Napoli 2-1, Feyenoord 3-1 and Manchester City 2-1.
The return leg between the Ukrainian and Italian clubs will be played at the Stadio Olimpico in Rome on March 13.
In another last-16 tie on February 21, Spain's Sevilla and England's Manchester United played out a goalless draw.
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