Just 57 seconds after Kieron Dyer fired United into a 52nd minute lead, a fatal moment of defensive slackness handed the Addicks an equaliser.
Dyer, the Magpies' best player on a frustrating day, chested down an Alan Shearer header and beat Dean Kiely from 12 yards with the aid of a deflection off Talal El Karkouri.
But as so often this season, Newcastle were at their weakest after scoring, and when Andy O'Brien failed to control a Hermann Hreidarsson pass on the edge of his own box, Dennis Rommedahl seized on the ball to make space and drill a superb 20-yard shot in off the base of the right post.
The goal was Charlton's first shot on target, which added to the despair of the home fans who had seen their own side take 12 goal attempts to score.
But after the two-goal flurry, Charlton were the stronger side and might have stolen victory when they created a string of chances.
On 74 minutes Rommedahl brilliantly tricked his way between Celestine Babayaro and Titus Bramble but from 15 yards chipped his shot past the sprawling Shay Given and beyond the left post.
Two minutes later, as Newcastle fell apart at the back, Rommedahl latched on to a Shaun Bartlett flick but Given stretched out his right leg to save.
Within moments Matt Holland shot just wide from the edge of the box, then right-back Luke Young dribbled past Babayaro but lifted a 14-yard shot over.
It was a total turnaround from the first half when Newcastle held the upper hand.
Kiely in the Charlton goal looked nervous at the start as he fumbled a sixth minute Shearer shot round the post, then failed to get his hands behind a surprise 35-yarder from O'Brien which dropped on to the top of the bar and over.
However, Kiely did well to hold a Shearer header and another long-range special from Lee Bowyer.
Charlton's only goal threat in a dour first half came when Danny Murphy shot well wide.
But all the action came after the break and as the prospects of victory receded Newcastle manager Graeme Souness sent on French winger Laurent Robert and Dutch international Patrick Kluivert for the last 20 minutes.
Kluivert and Shearer had shots blocked in a 87th minute scramble but amidst unrest from the home fans, Charlton held on for only their fifth league draw of the season.
MAN OF THE MATCH: Danny Murphy (Charlton Athletic) – Has been the catalyst for Charlton's recent revival and was once again behind much of the visitors' best work.