Roberto Martinez hailed an "historic day" as his Wigan Athletic side recorded their first victory at Anfield to boost their survival hopes on Saturday.
Shaun Maloney put Wigan ahead with a 30th-minute penalty after Martin Skrtel kicked Victor Moses in the face.
Luis Suarez equalised two minutes after half time, but the visitors bounced back with Gary Caldwell's winner just after the hour.
The victory, which extended Wigan's current run to one defeat in seven matches, ensured they closed the gap between them and safety from three points to just one.
"It is a historic day for us, Wigan beating Liverpool at Anfield," Martinez said.
"That is why we are involved in football, to defy the odds and history. I would like to present this moment to our fans, as they have not had much to celebrate this season." The result could have been different had Suarez's effort just a few minutes after his first goal not been ruled out for handball.
Martinez and Kenny Dalglish, the Liverpool manager, disagreed in their interpretation of referee Lee Mason's decision.
"I have seen the replay and it is clearly a handball," said the Wigan manager.
"I have had so many bad decisions this season I've always kept my mouth shut and today I will only concentrate and enjoy our victory.
"I think Lee Mason was a very strong referee and we were fortunate with that, as we all know Luis Suarez is an artist in getting free-kicks and good situations for himself."
Dalglish, who blamed his team's lacklustre performance yesterday on fatigue, took the directly opposite viewpoint.
"There is no rhyme or reason why the second goal should be chalked off when Luis challenged for the header," Dalglish said.
"It wasn't a handball. I must have a different television. It hit his shoulder as he turned to try to play it in."
Dalglish complained he had been forced to use several players in all three matches his team had played in the past seven days and said those exertions caught up with them. "I think they looked a bit tired," he said.
"We had a lot of possession in the game, we gave away the ball quite a lot in vital positions and it is not because they cannot play but tiredness.
"If you play Sunday-Wednesday-Saturday it is going to take its toll, and a lot of the lads have played three games. For us that would be a reasoning behind our own performance.
"We were disappointed because a lot of the final balls in good positions we didn't deliver and we put that down to tiredness."
The defeat was Liverpool's fifth in their past six league matches and the 10th of a league season that is threatening to go into free fall after just two victories since the turn of the year.
Asked whether he thought better performances were around the corner, Dalglish said: "I'm not clairvoyant.
ARSENAL 3, ASTON VILLA 0:
Arsenal Gibbs 16’, Walcott 25’, Arteta 90+3
Arsene Wenger hailed a “dynamic performance” after Arsenal strengthened their grip on third place.
“I felt it was a very dynamic, fluent performance in the first half with top technical quality," Wenger said. "It was a controlled performance in the second half, but our fatigue came in a bit because we gave a lot at Everton on Wednesday night. We have consistency at the moment, so let’s go home and wait for the next game.”
SUNDERLAND 3, QPR 1:
Sunderland Bendtner 41’, McClean 70’, Sessegnon 76’
QPR Taiwo 79’
Red cards Cisse (QPR)
Mark Hughes received a vote of confidence from the club owner Tony Fernandes, as QPR slumped into the relegation zone.
“The manager can do nothing if players keep getting sent off and booked,” Fernandes said on Twitter.
“Mark Hughes is right guy and he has my support. I can’t believe this. Red cards. Nothing to do with luck.”
NORWICH CITY 2, WOLVERHAMPTON 1:
Norwich Holt 26’, 45’
Wolves Jarvis 25’
Red cards Holt (Norwich)
Paul Lambert said Grant Holt’s sending off was harsh but was delighted with the win over Wolverhampton Wanderers.
Holt received his marching orders after collecting a second yellow card for a challenge on Michael Kightly.
“I thought the first one was a foul against him, so I don’t know what the referee has done there,” Lambert said. “The second one … Grant has won the ball.”
SWANSEA CITY 0, EVERTON 2:
Everton Baines 59’, Jelavic 76'
David Moyes hit out at the Premier League over Everton’s run of fixtures after watching them leapfrog Swansea on Saturday.
The Toffees are in the midst of a March that will see them play nine fixtures.
Saturday’s contest was their fourth game in just 11 days.
“The Premier League have not helped us out and I have been disappointed in them,” Moyes said.
“I don’t think they have been fair to Everton in many ways this season.”