The victory leaves Shakhtar on nine points from four matches in the pool, three behind leaders Manchester City but six ahead of third-placed Napoli, whom they play next in Naples on Nov. 21. Feyenoord have yet to secure a point.
The Dutch side took an early lead as Nicolai Jorgensen powered home a header but within five minutes their hosts had turned the match on its head as first Facundo Ferreyra equalised and then Marlos added a second with a curling effort from the edge of the box.
Feyenoord tried to play their way back into the game in the second half with a period of concerted pressure but were stung by a fine passing move from Shakhtar that ended with Marlos completing his brace to make the points safe.
(Reporting By Nick Said; Editing by Clare Fallon)
