Jurgen Klopp celebrated with his familiar fist pump in front of the away end as Liverpool made it seven wins in a row.
Victory clinched a European place for next season but they are now breathing down the necks of Manchester United and Newcastle in the battle for a Champions League place, now just one point off the top four.
But, in contrast, Leicester are sinking fast and even their fans have all but given up hope after another woeful surrender at the King Power Stadium.