Alex Oxlade-Chamberlain struck two long-range goals – his first strikes since April 2018 – to put the Reds into a two-goal lead.
Sadio Mane and Mohamed Salah further added to the scoreline, though Genk had something to cheer when Nigerian striker Stephen Odey grabbed a late consolation.
Liverpool now sit second on the table with six points and a point behind Napoli.
#UCL – RESULTS:
Slavia Praha 1-2 Barcelona
RB Salzburg 2-3 Napoli
Genk 1-4 Liverpool
Inter Milan 2-0 Dortmund
Lille 1-1 Valencia
Benfica 2-1 Lyon
