Both sides had chances after the restart, but neither was able to claim maximum points.
Here, Sports Mole has looked back over the action to determine whether or not either of the rivals deserved the victory.
On target 8
On target 5
Was the result fair?
All in all neither side can argue that they did enough to win this encounter. Liverpool controlled the opening exchanges, before Everton dominated the remainder of the half. There was very little to separate the two teams after the restart, although Liverpool will feel hard done by after seeing Suarez's late goal wrongly ruled out for offside.
David Moyes will be furious with the way that his side started, but at the same time he will be pleased with their response. One thing that appeared to hamper their performance was the half-time withdrawal of Kevin Mirallas, who had looked dangerous up until his ankle injury.
The Reds started the match like an express train but were soon pegged back. They didn't fold after Everton had drawn level though and regained an element of control in the second half. They also arguably had the better chances in the closing stages.
Sports Mole's man of the match
Luis Suarez: Love him or hate him, Suarez was a constant threat to Everton as a lone striker today. He caused the first goal that went into the net off Baines, before going on to get a goal of his own. He would have had a second in stoppage time but for an incorrect offside flag.
Raheem Sterling has been impressive since he broke into the Liverpool senior side but he will want to forget about his shot early in the second half. Jose Enrique slotted him through one-on-one with Tim Howard, but with time and space he scuffed a shot well wide of the target when it looked easier to score.
In such a fiercely-contested fixture Andre Marriner did well to keep the players calm. There were very few incidents off the ball, which Marriner has to be given credit for. The decision to rule out Suarez's late strike had nothing to do with him.
Everton: Next Saturday Everton travel down south to take on Fulham.
Liverpool: Following a Capital One Cup tie with Swansea City during the week, Newcastle United make the trip to Anfield on Sunday afternoon.