Liverpool won the Merseyside derby 2-0 thanks to a brace from Mohamed Salah in a game where Everton were forced to play with 10 men for an hour after Ashley Young's sending off.
Young was red carded following two debatable first half bookings, while referee Craig Pawson further enraged the visitors with his failure to send off Ibrahima Konate in similar circumstances in the second half. Already on a yellow card, Konate tripped substitute Beto as he looked to race clear on halfway. Reds boss Jurgen Klopp responded to Konate's reprieve by immediately subbing the French defender.
Liverpool eventually broke Everton's stubborn resistance with a Salah penalty awarded for a handball by Michael Keane, and a second Salah goal followed in the dying moments as the visitors over-committed in search of an equaliser.
Everton manager Sean Dyche labelled the officiating "bizarre" and the decision not to send off Konate as an "impossibility of football".
"I asked the referee and he said he didn't think it was a bookable offence. Jurgen couldn't wait to get him off," said Dyche. "That decision was incredible to me, and I got a yellow card. It was ridiculous."
Young’s 37th-minute red card – the 29th in this fixture and the 13th of the last 16 to be shown to Everton players – came with Liverpool on top, but was contentious.
Luis Diaz looked to have somewhat bought the first yellow when he went down after a tackle on the halfway line and the second was harsh as Young mistimed a tackle with Diaz on the attack near the Everton box.
Dyche’s response at half-time was to replace his two wingers – Jack Harrison and Dwight McNeil – with defenders Nathan Patterson and Michael Keane and switch to a back five.
Klopp’s side were nowhere near their best in the final third and that played into Everton’s hands.
Konate, whom Everton’s coaching staff felt should also have had a second yellow card for a foul on Beto, was removed for his own good.
Keane must have wished he could have been afforded the same courtesy when his loose arm blocked Diaz’s cross.
Pawson initially gave a corner but VAR advised him to review the pitchside monitor and he reversed his decision and Salah sent Jordan Pickford the wrong way from the spot.
Harvey Elliott and Jota both went close as the onslaught continued but it was Salah who benefited from Darwin Nunez’s quick counter-attack as he clipped home his second as Liverpool extended their record to one defeat in the last 28 derbies.
Liverpool captain Virgil van Dijk credited Everton's resolve and admitted it became difficult to play against 10 men.
“In my opinion the hard work came form the fight Everton put in," he said. "The long balls, the set pieces, they tried to counter on us but we were very prepared for it. The message was to stay patient and play quick from side to side. They made the change at half-time to play with five at the back and we had to be more patient.
“It is difficult to face teams playing with 10 men. We have been on the other side and done well. Our mindset was they were still playing with 11 because it is a bit of mental thing when you have a man extra."
Klopp admitted his side had gotten the rub of the green.
“I liked a lot of moments and then the red card was pretty influential in the game," he said.
"I wanted us to be calm and ignore that we were one man up. It is difficult in the stands because it’s like now you have to create with each possession and it took a while until we got chances. And then the penalty. I saw it back and it is a clear penalty. Ibrahima [Konate], could have gone, yes. It could have happened obviously and then we took him off and from that moment we were solid and compact.”