The match took place at Borussia-Park in Monchengladbach on November 25, according to Ukrinform.
The goals were scored by Lars Stindl (17), Nico Elvedi (33), Breel Embolo (45+1) and Oscar Wendt (77).
In another Group B match, Italy's Inter lost 0-2 to Real Madrid in Milan.
Borussia are on top of their group with eight points from four games. Real are second with seven points, followed by Shakhtar with four points, and Inter with two points.
In the next round, Shakhtar will host Real on December 1.
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