Dean Ashton wasted a golden opportunity at the end of the first half and when substitute Svensson failed to beat Dean Kiely after coming on as a late substitute it looked as if there would be no late show for City's fans this time.
Then, two minutes from time, up popped former Charlton star Svensson who made no mistake with a volley which was enough to grab all three points and once again boost the Canaries hopes of Premiership survival.
Charlton forced two early corners but the first real threat came from the Canaries when Mattias Jonson headed David Bentley's cross into the safe hands of Kiely.
Robert Green had to move quickly to beat Francis Jeffers to a throughball while at the other end Leon McKenzie's dangerous cross was headed behind by Jonathan Fortune.
Norwich's man of the moment Ashton had his first chance of the game just before the half hour, but his shot found the back of the stand.
In the last minute of the first half McKenzie's header released Ashton but the in-form striker fired wide with only the keeper to beat.
This miss could have proved costly because the Addicks stepped up the pressure early in the second half and Green did well to keep out a stinging shot from Talal El Karkouri, before Dennis Rommedahl brought a smart save from Green.
Youssef Safri, scorer of a spectacular goal in midweek, fired over after a good spell from the home side.
Jason Shackell, outstanding in the City defence, then stretched his neck in the Charlton penalty area but could not make contact with Safri's free-kick.
Darren Huckerby, on for Jonson, put in a telling cross which was grabbed by Kiely before it reached McKenzie. The Charlton keeper then did well to block Svensson's shot in a one-on-one situation.
Danny Murphy's deflected free-kick came back off a post and the resulting danger was cleared by Svensson.
With the seconds ticking away, Adam Drury took a throw in level with the Charlton penalty area. Ashton and McKenzie headed the ball on and when it bounced in front of Svensson he rifled a right-foot volley which beat Kiely's despairing dive.
Man of the Match - Jason Shackell
Jason Shackell put in another solid performance at the heart of the Norwich defence, belying his tender years with a mature approach to the game and making the Charlton forwards look decidedly ordinary.