The game's turning point came in the 12th minute when Javier Mascherano's shot from 25 yards took a deflection off Nigerian defender Joseph Yobo and beat American Tim Howard to give the Reds the lead.
"The deflected goal took the sting out of us," said Everton manager David Moyes. "I don't know how many times Liverpool had been in our half up to that point but it wasn't many. I thought the players reacted great. They kept going and I thought in the main we kept Liverpool quiet. The game was tight and we, in the main, were trying to set the tone and make it difficult for them."
Everton had its chances, but Russian Diniyar Bilyaletdinov missed twice, and Liverpool goalie Pepe Reina did well to stop Tim Cahill and Marouane Fellaini.
With 10 minutes to play, Liverpool put the game away when Dirk Kuyt scored on a rebound after Howard parried Albert Riera's shot. Yobo was to blame for the goal, failing to clear a ball that Steven Gerrard picked up and fed to Riera.
The win, which came just five days after Liverpool was knocked out of the UEFA Champions League, was comfort to Liverpool manager Rafael Benitez.
"It was a clearly a difficult game from the beginning," said Benitez. "They were playing a direct and also a set-pieces game. It was very difficult to control that because they are strong in the air but we showed character and were trying to play counterattack -- sometimes with good possession, sometimes not so good."