Daniel Sturridge's 100th club goal provided the crucial breakthrough five minutes after the break and Roberto Firmino and Georginio Wijnaldum made sure of the points after Mohamed Salah had missed a penalty at the end of the first half, which was followed by boos by disgruntled fans.
"The manager told us not to get frustrated because they were dropping real deep", Wijnaldum said.
Liverpool's home form contrasts sharply with their away results and they have now conceded only once at Anfield compared to the 15 they have let in on their travels - the most recent setback being last week's 4-1 loss at Tottenham Hotspur.
"Every win is a big win for us and it was important because we had to give a reaction from the match last week".
"We'll make the decision after training today". I could hear it. People didn't like the first half too much.
"That's how it looked a little bit in the first half, so it was not too hard to fix at half-time". It was not fluent, we had too many players behind the ball, it was clear we wanted to give them no opportunity for counter-attack and stuff like this, but you don't need seven players behind the ball to protect the counter-attack. The second one after a set-piece felt like Christmas.
"I am disappointed because the players have given good effort and worked hard".
We still suffer from the same age old problems of having a poor goalkeeper and a bad defence that ships goals galore.
The result had looked far from secure after a terrible first half, watched by the president of club owners Fenway Sports Group Mike Gordon who had flown in for the game.