Five minutes later, Klopp’s men should have added to it when Jordan Henderson curled a beautiful ball to the far post only to see Adam Lallana steer his stooping header wide from a couple of yards out.
In the 27th minute Liverpool grabbed a second and this time Bywater had to shoulder some of the blame when he threw the ball out straight to Mane.
He sent Nathaniel Clyne racing down the right and when the full-back swept his cross over there was Firmino unmarked to power home a close range header.
Clough’s men harried and chased and though they forced a brief flurry of corners, they were struggling to trouble Simon Mignolet in the visitors’ goal.
But on the hour Liverpool effectively killed the tie off when Burton got in a pickle from a James Milner corner and Tom Naylor got the final touch into his own net.
Sturridge added a fourth on 75 minutes when he rammed the ball home from close range from Milner’s low cross and helped himself to another near the end with a crisp left foot shot.