The goals at the Stadion Feijenoord were scored by Feyenoord's Steven Berghuis (7th minute) and Shakhtar's Brazilian Bernard (24, 54), Ukrinform reports.
Shakhtar's Yaroslav Rakitsky was shown the red card in the 75th minute.
The match was handled by a team of Spanish referees headed by Alberto Undiano Mallenco.
In another Group F match, England's Manchester City beat Italy's Napoli 2-1 at home.
Group F standings: Manchester City - 9 points, Shakhtar - 6, Napoli - 3, Feyenoord - 0.
Shakhtar will play its next match against Feyenoord in Kharkiv on November 1.
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