Peter Whittingham almost doubled Cardiff's advantage on 22 minutes, but Hamer produced a good stop to keep out his left-footed drive.
It was only a matter of time before Malky Mackay's team extended their lead, and they did just that in the 24th minute. Helguson was the provider this time, lining the ball up for Joe Mason to smash in from close range.
Cardiff were left kicking themselves at the stroke of half-time when they allowed Charlton to draw level. Salim Kerkar whipped in a corner and Jackson pounced for his second of the night, making it 2-2 at half-time.
Whittingham almost put the visitors back in front just after the interval, with Hamer tipping his low shot around the post, but the second half would be an entirely different story.
MacKay's men fell behind in the 56th minute to a Dale Stephens strike from more than 35 yards back.
Fives minutes later it was 4-2, as Bradley Pritchard played in Danny Haynes on the right and the midfielder placed his shot straight into the centre of goal.
Charlton were a dominant force in the second half, and they got their fifth on 65 minutes when Kerkar's cross was headed in to the lower right corner by Rob Hulse from six yards out.
Noone ensured a dramatic finish when he latched onto Dave Marshall's long-range pass to bundle the ball home in stoppage time, and there was more drama to come.
Aron Gunnarsson found the net in the 95th minute to add another consolation, but a fifth was a bridge too far for Cardiff in this roller-coaster ride.