Red Star Belgrade butchered a surprise chance to go ahead at Anfield, and the hosts made them pay within moments.
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Shaqiri starts the play with an interceptions, then playing an inch-perfect pass into the box for Robertson.
The Liverpool left back cuts a ball toward the spot, and Firmino takes a touch before his slightly-deflected shot wrong foots Canadian keeper Milan Borjan to put the Reds on top.
A win guarantees Liverpool a spot in Group C’s Top Two at the midpoint of the group stage.