Fabio Borini, making his home debut for the club, had an early chance to put Liverpool ahead but his shot was blocked well and Gomel keeper Vladimir Bushma was alert to keep out Luis Suarez's effort from the rebound.
However, Borini didn't have to wait long for a second chance and this time he made no mistake as he pounced on a loose ball in the box to fire his shot past Bushma.
The first goal was vital for Brendan Rodgers's side as Gomel looked to be struggling in front of the Kop and the Reds were further ahead before the break when Suarez attacked at speed before picking out Steven Gerrard, and the skipper finished easily from inside the box.
Gomel started the second half well but Suarez had the best of the chances after the interval when his powerful effort was saved well from Bushma.
Liverpool extended their lead with 18 minutes remaining when Glen Johnson unleashed a half-volley from outside the area that left Bushma helpless to complete an impressive performance from the England right-back.
Gomel defended defiantly in the final stages to keep the score respectful but the Belarusian side couldn't find a goal of their own as Liverpool comfortably progressed.