A solid defensive display was compounded by an assured return from Uruguayan Gonzalo Sorondo.
Jerome Thomas and Jonathan Spector were on the receiving end of strong challenges early on and it was the visitors who started the livelier.
Clear openings were at a premium and as the midway point of the first half approached neither side had carved out a shooting chance.
It was in the closing stages of the first half that Everton enjoyed the game's best moment so far.
The hosts looked the side most likely to score in the closing stages of the game as pot shots continued to flow at either end. But at the death, in truth, a goal never looked like coming after a contest that will probably be forgotten by most before they exit Floyd Road.
In a game so starved of clear-cut chances the game's most significant moment came courtesy of a sticky moment from Toffees keeper Richard Wright, who was a relieved man after an amazing blunder.
Shaun Bartlett and Darren Ambrose were added to the bench with England pair Darren Bent and Luke Young both out of action. Jonathan Spector filled in for Young, while Jay Bothroyd started in place of Bent. Jason Euell was a straight swap meanwhile for injured Bryan Hughes, while Gonzalo Sorondo returned in place of Chris Powell. Jerome Thomas was promoted from the bench to replace Dennis Rommedahl who started among the substitutes.
The draw meant Charlton failed to make up any ground on Everton who remain a point clear. Meanwhile, Newcastle United took the advantage earning three points over the weekend to move above both clubs.
Alan Curbishley: "I thought we just shaded it today. Everton's form has been terrific since the turn of the year and it was always going to be difficult, but we just couldn't force the goal to open the game up. In the last seven Premiership games it's only been Arsenal that have hurt us and they're hurting everybody at the moment."
"I made five changes today from the West Ham game for the right reasons. I made one tactical change, Jerome Thomas for Dennis Rommedahl, and I rested Darren Bent and Chris Powell. I rested Darren because if something had happened to him, both he and Marcus [cup-tied] would be out for Wednesday. Chrissy would have found four games in ten days difficult. But I was pleased to see Jonathan Spector at right-back and I've been desperate to see Gonzalo Sorondo play again and they both had the chance to start today."
Curbs on Luke Young's injury one week on: "He had a similar injury last season and was out for about six weeks but we felt we might not have treated it properly then."
Curbs on Bryan Hughes's injury: "Hughes hurt himself in training; he has a badly bruised foot."
Matt Holland: "It was a tough game, and frustrating because I thought we edged the match without dominating it. Another 0-0 keeps us unbeaten at home since Christmas but we would have liked to have won and moved above Everton. It wasn't to be though - enough balls went in the box but it didn't quite happen for us. But there was a good defensive attitude about the players; everyone wanted to get goalside of their men and dig in."
"It looked like the goalkeeper was going to pick it up, and we were heading back to the halfway line, but suddenly he was scrambling back towards his own goalline and just managed to palm the ball wide. I think most people had turned around, even myself. It certainly would have been the most bizarre goal I've ever scored."
Richard Wright (EFC): "It was a difficult game because they were putting a lot of balls in the box."
Source: Official site