But the Londoners are likely to find out that just securing one point at home will not be enough for them to escape the relegation trap-door at the end of the season.
Having taken just a single point on their travels this season it is vitally imperative that Charlton win their home games. For long periods of this match they looked as though they would be beaten by an Everton side who passed the ball with more confidence, without having the cutting edge they needed due to the surprise absence of Andy Johnson up front, who had to drop out with a hamstring injury sustained in training on Friday.
It was typical of a team's luck when they are struggling that Charlton should have gone behind from an own goal, but they showed plenty of spirit and endeavour if lacking in quality to get themselves back into the game.
In a hectic finish to the match, they might have snatched victory had they showed more composure in front of goal and their final ball let them down time and time again.
Sensing that Charlton would be nervous, Everton flew out of the blocks and had a couple of early chances when Lee Carsley's shot was deflected for a corner and James McFadden was denied by a great defensive tackle from Talal El Karkouri.
When Charlton did eventually get into their stride, Dennis Rommedahl saw his effort deflected and Andy Reid forced the first save of the match for Toffees keeper Tim Howard.
After a goalless first half, Everton took the lead in fortunate fashion when Mikel Arteta's free-kick ricocheted off Charlton defender Hermann Hreidarsson and deflected past his helpless goalkeeper Scott Carson.
At this stage the strugglers could have collapsed, but to their credit they kept going and when former Everton player Marcus Bent came on as substitute to give some support to his namesake Darren, it was the home side who looked the more likely to snatch victory.
Charlton got their equaliser when Everton failed to clear a long ball and Reid, who was Charlton's inspiration in midfield, fired low into the net.
Goalkeeper Howard had to make a fine save to palm away another Reid effort and in injury time, the normally on target Darren Bent, fired over the bar from a good chance.
After all the turmoil of the last couple of weeks following the departure of head coach Iain Dowie, Charlton's new man at the helm - Les Reed - would have been hoping to get off to a winning start.
He couldn't have asked more from his team in terms of spirit and endeavour, but they are finding goals difficult to come by and the frustrating Rommedahl, whose pace terrorised the Everton defence, once again failed to produce an end product.
Everton will probably feel that they should have wrapped the game up in the first half.