Sadio Mané struck in the fourth minute of injury time to win one of the most forgettable Merseyside derbies in recent memory, but did leave them second in the Premier League.
The Merseyside derby came at a time of opportunity for Liverpool, who were able to go second on their own with victory due to Arsenal's choke away at Manchester City. Everton, meanwhile, were hoping to pick up another big scalp at home after beating the Gunners on Tuesday.
A passionate atmosphere was raised at Goodison Park for the grudge match, with Liverpool's line-up loudly booed and the Toffees roared on 'early doors' by the home faithful.
Their energy was boosting Everton, who threatened the Reds defence with a breakneck tempo enforced by a positive Idrissa Gueye. Dejan Lovren and Ragnar Klavan were the men tasked with weathering the storm, but struggled to find other red shirts for all their defensive calmness.
It took twenty-five minutes for Liverpool to find a way into the game, but they only had a couple of wild Georginio Wijnaldum shots to show for it. The final ball was wasteful under Everton's hard-tackling pressure.
A decent chance fell at last, and it came to the away side. Nathaniel Clyne squared the ball across the box, but Divock Origi hooked it over the bar. Finally, an event worth talking about.
Ramires Funes Mori recorded Everton's first meaningful attempt with a clear header from a corner. Wide it bounced, and that was effectively it for the first half. A third consecutive half in derby matches involving Liverpool was unexpectedly, and painfully, boring.
Roberto Firmino was one-on-one with Maarten Stekelenburg early in the second half, but the goalkeeper spread himself well to make a save. The Reds had turned the early tide and were beginning to dominate the game.
The first yellow was handed out in a match which has historically seen more red cards than any other, by a referee who has handed out more reds than any other this season, after fifty-five minutes! Lovren had fouled Romelu Lukaku.
Stekelenburg collided with Leighton Baines, and the injury forced him off. Joel Robles would make a rare appearance in his place. Meanwhile, Ross Barkley lunged into a heavy challenge on Jordan Henderson's ankle - the tackle was vicious enough for a red, but a yellow was given.
Firmino fired a volley from a corner, but Robles passed his first test with a good save. Liverpool were on top and their hosts could only defend deep, but clear chances were still evading their frustrated visitors. Emre Can's horrifically overhit pass into the stands summed it up.
There were eight minutes of added time for Liverpool to find a winner. The fourth was the one that won them the game, with Daniel Sturridge striking the post and the ball bouncing back to Sadio Mané. A simple tap-in brought delight from the away end.
Unfortunately, it also brought red flares and a pitch invader onto the Everton pitch, leaving everybody with a sour taste after an important win for Liverpool.