The result sees second-placed Liverpool close the gap to the Premier League leaders Manchester City to one point.
The defeat leaves Frank Lampard’s side in the relegation zone after Burnley leapfrogged them with a 1-0 win over Wolves earlier on Sunday.
Both teams failed to create many clear-cut chances in the first half as Everton set up to frustrate Liverpool with a defensive set up.
The biggest flashpoint came just before the break as both sets of players clashed after Liverpool failed to put the ball out after Richarlison went down injured.
Liverpool finally broke the deadlock after the hour mark when Robertson headed home from Mohamed Salah‘s floated cross.
With five minutes remaining, substitutes Luis Diaz and Origi combined to double the lead for the hosts and keep them in touch of Pep Guardiola’s side in the title race.