The Foxes had the better of the opening exchanges with Shinji Okazaki firing over from 20 yards but just before the quarter-hour mark, Liverpool went ahead thanks to a fine finish from Roberto Firmino.
The opener sparked a spell of Liverpool dominance and after Georginio Wijnaldum had curled over, Daniel Sturridge was left wondering how he had not added a second for his side as Kasper Schmeichel pulled off a save at point-blank range after the forward had been found by Sadio Mane.
However, the home side did not have to wait much longer for another goal as Sturridge produced a back-heel into the direction of Mane, who flicked the ball over Schmeichel from inside the area.
Liverpool were in total control but with seven minutes remaining before half time, Leicester were gifted a way back into the match when Lucas Leiva miscontrolled the ball inside the penalty area before poking it into the path of Jamie Vardy, who fired home into an empty net.
Moments later, the two teams could have been back on level terms after a long throw from Luis Hernandez found Huth, whose header cannoned back off the crossbar after Simon Mignolet had missed his punch.
Leicester had the better of the play after the restart but 11 minutes into the second half, they conceded a third as Adam Lallana rifled the ball into the top corner after a neat layoff from Wijnaldum.
The goal led to Liverpool pushing forward in search of a fourth, but Leicester almost halved the deficit for a second time when Riyad Mahrez played in Vardy, although last season's top goalscorer was denied by Mignolet.
As the game entered the final quarter, Leicester threw more men forward in search of a second goal but despite enjoying more joy in the final third, only a volley from Danny Drinkwater came close to finding the back of the net.
With 10 minutes left, Jordan Henderson had the chance to put the game to bed with a half-volley from eight yards out but he could only drive the ball high over the crossbar.
Liverpool finally netted a fourth a minute before the end of normal time when Mane latched on to a long ball and after beating Schmeichel to Henderson's pass, he remained patient before teeing up Firmino to complete the scoring in what was a dominant performance from the Reds.