The Owls had lost their previous seven games in the npower Championship which left the former Cardiff boss clinging on to his job, but Chris O'Grady's first-half goal earned the vital points and stopped the rot.
The goal was shrouded in controversy, though, as O'Grady tapped home after Barnsley goalkeeper Luke Steele had dropped the ball under the challenge of Gary Madine, with television replays showing a push.
Wednesday rode their luck in holding on for the win and Keith Hill's men will feel hard done by in losing a game they controlled for large parts as Marcus Tudgay could have had a hat-trick of headers.
The Owls will not care about that, though, as they moved off the bottom of the league and joined Barnsley on 18 points.
While Jones will be breathing easier, the same cannot be said of Hill, who is coming under the cosh from Reds fans unhappy at an 11-game winless run. His future could be decided after the Christmas period.