An Aleksander Mitrovic brace and a Nemanja Radonjic strike secured the win for Serbia, only their second success of the Euro 2020 qualifiers.
Last Saturday, Serbia fell 4-2 to Portugal, with Milivojevic playing 87 minutes before being replaced by Luka Jovic.
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The victory over Luxembourg marks the end of Serbia's fixtures until October 14th, when they play Lithuania. They currently sit third in Group B, just one point behind Portugal.