Everton fans taunted Liverpool supporters suffering a miserable evening at Goodison Park by mocking the Reds for slipping up in the Premier League title race.
Shock defeat in the Merseyside derby gives Liverpool a mountain to climb as Jurgen Klopp's side remained three points behind leaders Arsenal and only one point clear of Man City who have a game in-hand.
Liverpool's forwards were ineffective against cross-city rivals Everton, while the visitors defence was broken as Jarrad Branthwaite and Dominic Calvert-Lewin got on the scoresheet.
The Reds were previously unbeaten at the home of their rivals since 2010 when Everton similarly ran out two-nil victors on that occasion as well.