Wigan were lacklustre for an hour but the threat on the Norwich goal grew and grew and, after Antolin Alcaraz had seen a header cleared off the line, it was Kone who fired home nine minutes from time from the edge of the box after he was picked out by Jordi Gomez.
The win sees Roberto Martinez's side climb above Aston Villa on goal difference with 30 points, four behind Norwich.
Last season a point at Carrow Road in March provided the impetus for the Latics to win seven of their last 10 games and engineer a great escape and Martinez will be hoping for more of the same with three league wins now out of their last four matches.
The visitors are also not clear of the relegation scrap and they began well, with striker Kei Kamara looking a threat, but they did not trouble Joel Robles in the home goal.
The hosts were also struggling to make an impact but they did put together a fine move in the 27th minute as Shaun Maloney turned and found Emmerson Boyce who set up Kone for a shot just wide.
Alcaraz had been a doubt for the match, with Martinez keen not to overplay him after he missed six months of the season with a groin tear, and the Paraguayan's calmness in defence has been much missed.
This was shown when he saved his team after a misunderstanding allowed Kamara to run free only for Alcaraz to nick the ball quite brilliantly.
Wigan went down the other end and again it was Kone with the shot, which was parried away by Camp, although it may have been going wide anyway.
In the second period, Maloney worked himself into a great position from a corner but fired a long way over the bar while, at the other end, Bradley Johnson was much closer with a shot just past Robles' post.
Alcaraz then rose highest to meet Jean Beausejour's corner but his header was cleared from near the line by Jonny Howson.
The Wigan goal was coming and, after James McCarthy's shot went just wide, it arrived in the 81st minute after Wes Hoolahan lost the ball in midfield.
Gomez did well to pick out Kone, who smashed home from the edge of the box to seal a massive three points for the Latics.