Substitute Tony Watt and Igor Vetokele were Charlton’s second-half scorers after Jonny Howson and Lewis Grabban had given the Canaries a deserved half-time lead.
The stirring comeback was a big relief for new Charlton head coach Guy Luzon, who had been barracked by the home fans in the first half.
But Jerome converted a cross from fellow replacement Wes Hoolahan with seven minutes remaining to give play-off hopefuls Norwich the points and leave Luzon a loser after all.
Norwich dominated from the off and it was no surprise when they took the lead in the 14th minute.
Grabban’s simple pass set up Howson, who had all the time and space he required to slot the ball beyond the reach of home goalkeeper Marko Dmitrovic. Bradley Johnson, who had earlier fired wide from distance, also deserved plaudits for winning the ball to set up the chance.
Nathan Redmond was looking lively and the Norwich winger fired off a shot that Dmitrovic was able to get behind.
Charlton were all over the place and Johnson fired wastefully over from the edge of the box at before failing to connect right in front of goal as he slid in to meet a ball from Grabban, who had slipped past the home defence on the right.
Norwich doubled the lead in the 43rd minute when Grabban was sent beyond the home defence and, as Dmitrovic came rushing out, the forward had the presence of mind to loft the ball over the goalkeeper and into the empty net.
The home fans turned on Luzon, singing that he would be ‘sacked in the morning’ and booed the players off the pitch at half time.
Luzon made a change at the break, replacing the ineffectual Frederic Bulot with forward Watt, but Norwich carried on where they had left off, with Johnson heading wide from a cross from Steven Whittaker.
Charlton had to soak up more pressure and replaced Jackson with Callum Harriott before Watt’s introduction paid off with a 61st-minute goal after Vetokele had flicked the ball into the Scot’s path.
It was a first Charlton goal for the 21-year-old since leaving Standard Lierge last month.
The home side were level in the 68th minute when Vetokele found the net after Norwich goalkeeper John Ruddy had parried an effort from Harriott.
Both sides created chances and it was Norwich who finally took one, with Jerome’s header bouncing over the line in the 83rd minute.