It was just not Palace's day with Aki Riihilahti rattling the crossbar and then Dean Kiely pulling off a great penalty save to prevent leading scorer Andrew Johnson putting Palace ahead early in the second half.
A rather ordinary first half saw the Addicks look the slightly better side and they should have gone in front at the half-time whistle when in stoppage time Jerome Thomas made tremendous ground down the left and a goal looked on, but the ex-Arsenal youngster forced Gabor Kiraly into making a great reflex save.
It was in fact the only creative opening in the first 45 minutes although Riihilahti provided the Eagles' best effort with a powerful header from Joonas Kolkka's fine run down the left side.
That apart, Palace were certainly firing blanks as Johnson was being well watched by Jonathan Fortune with help from fellow defender Radostin Kishishev.
However outside the box Johnson was proving a real handful and suffered rough treatment with some over-zealous tackling. Indeed Fortune went into the referee's book after only 11 minutes as the Palace leading scorer caught out the Charlton defence with his acceleration.
Johnson was offered just one chance and a difficult one at that when a Wayne Routledge corner skimmed the top of his head and Charlton were able to clear their lines.
Skipper Matt Holland struck a rocket header from Thomas' cross which Kiraly was relieved to watch flash past the far upright.
Palace started the second half a little better and their persistence paid off after 58 minutes. Ben Watson picked up a loose ball in the centre circle and after being given a bit of rare space, laid on a great pass to send Johnson away.
The Palace hitman galloped into the box, sped past Talal El Karkouri before being hauled down by the Moroccan international.
El Karkouri got booked for the offence as Charlton argued the decision. After a short delay, Johnson stepped up to take the kick, it was driven low and hard but Kiely made an outstanding save at the foot of his left post.
Palace tried to keep the tempo up as Kolkka let fly with a tremendous shot which produced another great save from Kiely.
At the other end, Charlton replied as Holland tried a snap shot which fortunately for Palace fell straight into the arms of Kiraly.
Johnson was still Palace's livewire and this time he burst through the Charlton defence and Kiely again came to the rescue with a brave stop at the feet of the Palace striker.
Kiely was then in action again after his defence badly misjudged a long clearance which allowed Johnson another good chance, but the Irish keeper was again in good form.
Still the Addicks were holding out and Hermann Hreidarsson did well with a vital clearance at the near post after Routledge hooked over a dangerous cross from the right.
Then came the sucker punch. With two minutes of injury-time already played, Palace made their first defensive error and a crucial one it proved.
Danny Murphy in the centre of midfield, passed over to the right to Rommedahl. It wasn't a particularly good pass but Danny Granville hesitated in cutting it out and suddenly the Dane grabbed his chance by drifting pass the stranded Palace defender and then letting fly with a tremendous low right-foot shot which gave Kiraly no chance as it flew past his outstretched left hand.
An unbelievable finish to the match, disbelief in the Palace camp, but jubilation for the 1,660 travelling Charlton fans.