Goals in each half hauled the Tykes off the foot of the table and to within two points of their opponents, who remain just above the drop zone.
Charlton, knowing victory would lift them up to 17th and drag the likes of Blackpool and Birmingham into the scrap at the bottom, were the dominant team throughout.
But their season-long goalscoring problems cost them yet again and they had only Astrit Ajdarevic's stoppage-time consolation to show for their efforts.
They bossed the first half-hour, with Jordan Cousins firing an early chance across goal before Johnnie Jackson just failed to connect with a dangerous cross from Callum Harriott.
Winger Harriott was guilty of their worst miss, though, when he somehow headed Marvin Sordell's cross wide from all of six yards out.
The Tykes, by this time, had barely set foot in Charlton's half.
But if the Addicks' lack of goals has been their Achilles heel this season, their defending from corners has not been much better.
So there was an air of inevitability around The Valley when, from their first real attack, Barnsley forced a 32nd-minute corner.
Dale Jennings swung the ball across and Mvoto, the French defender built like a cruiserweight boxer, caught Charlton with a sucker punch as he powered a header downwards and past the helpless home keeper Ben Hamer.
With the stakes high for both sides tempers flared before the break when Cousins and Stephen Dawson squared up to each other on the touchline.
They had to be separated by players and staff from both sides before escaping with a booking each.
Charlton came out on the attack after the interval and Diego Poyet whistled a shot narrowly wide in the opening seconds.
Sordell curled another effort well wide and the striker was then thwarted by a well-timed tackle from Mvoto in the area.
But from out of the blue, in the 63rd minute, Barnsley struck again when Kennedy's cross evaded everyone, including Hamer, before finding its way into the back of the net.
Substitute Ajdarevic bundled in a corner in stoppage time but their was no way back for the Addicks, who remain very much embroiled in a relegation scrap destined to go right down to the wire.