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 another great escape - and today's three points lifted them out of the Barclays Premier League's bottom three.
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 from the edge of the box.
Martinez stuck with the same side that beat Newcastle two weeks ago, which meant a second Premier League start for striker Callum McManaman.
The 21-year-old has been at the centre of a furore following his knee-high tackle on defender Massadio Haidara, which went unpunished both during the game and subsequently.
Wigan have been unhappy with the vilification of their player and it looked like an ankle injury might keep him out of the spotlight, but he recovered in time.
Martinez's selection meant number one goalkeeper Ali Al Habsi and captain Gary Caldwell again had to settle for spots on the bench, while Norwich were forced into one change with Lee Camp taking his place in goal for the suspended Mark Bunn.
There were some half-hearted jeers for McManaman from the Norwich fans and the striker might have answered them in the best possible way within three minutes but Javier Garrido pipped him to Jean Beausejour's cross.
The visitors are not quite 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.
Indeed, Sebastien Bassong failed even to trouble the corner flag with a horribly sliced effort in the 19th minute, much to the delight of the Wigan fans.
The hosts were 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.
McManaman had been a peripheral figure, although he should have registered a shot on target in the 34th minute when he was picked out by Beausejour but snatched at it.
Alcaraz had also 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.
The Paraguayan's calmness in defence has been much missed and 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.
It was the same Latics side that tore apart Everton in the FA Cup quarter-finals and they needed some of the same spark in the second half.
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.
McManaman's afternoon ended in the 67th minute when he was replaced by James McArthur and the hosts came extremely close to taking the lead three minutes later.
Alcaraz rose highest to meet Beausejour's corner but his header was cleared off the line by Jonny Howson.
Wigan were certainly in the ascendancy, with Maloney at the centre of everything, and they went close again in the 77th minute as James McCarthy drilled a shot just wide.
Jordi Gomez was the next to try his luck when he was picked out by Beausejour but his first touch was poor and the massed ranks of Norwich defenders blocked his effort, albeit with a hint of handball.
The goal was coming and it arrived in the 81st minute. Wes Hoolahan lost the ball in midfield and it proved costly as Gomez picked out Kone, who smashed home from the edge of the box.
It was a fine strike by the Ivorian but Camp will feel he should have done better at his near post.
Norwich could not exert any real late pressure on Robles' goal and Chris Hughton's side are now only four points ahead of their opponents.