The Londoners took their unbeaten run to four matches and gained their first back-to-back wins in 65 Premiership matches at the most crucial time of the season.
They are just one point behind Sheffield United and three behind Wigan as the battle to beat the drop looks like going to the final game of the season.
The match was tension-packed with neither side able to create any clear-cut chances and neither goalkeeper had a decent save to make, as the two defences dominated the game.
Charlton's first clear-cut chance of the match came from the winner, their 86th minute spot-kick converted by their skipper Darren Bent, for his tenth Premiership goal of the season.
The penalty was awarded after Charlton defender Hermann Hreidarsson, who was up in an attacking position, was bundled over by Fitz Hall after Wigan failed to deal with a long ball out of the Charlton defence.
Before the penalty Wigan looked the more likely side to score from the half-chances that they created, Caleb Folan firing over the bar and having another shot blocked.
For Charlton, Darren Bent headed wide and Jerome Thomas shot across the face of goal in the few chances that either side created.
The goal that Wigan conceded was their first in over seven hours of Premiership football, but it could prove a very costly one come the end of the season.
With fellow-strugglers Sheffield United still to come to The Valley and Charlton picking up a head of steam there is real hope that Alan Pardew's side can pull off safety which looked impossible a few weeks ago.
After their recent good run of results Wigan will be disappointed to have lost the match in the manner in which they did.