Wednesday went into the game with their fellow strugglers propping up the table - but banked a precious three points thanks to O'Grady's goal on 35 minutes.
The Owls had lost their previous seven games in the Championship which left the former Cardiff boss clinging on to his job, but 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.
While Jones will be breathing easy tonight 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.
It was no surprise that there was not too much quality on show early on given the respective poor runs of their sides, though a rasping drive from Stephen Dawson stung the palms of Chris Kirkland as Barnsley attempted to gain the initiative.
Neither side could wrestle control, though with no love lost between these two clubs - separated by just 13 miles - there was plenty to keep referee Stuart Attwell busy as the tackles flew in.
With Barnsley enjoying a spell of possession, Wednesday stole the lead 10 minutes before the break. Lewis Buxton found space down the right and delivered a searching cross that under duress from Madine's challenge Steele dropped and O'Grady turned into an unguarded net.
Steele was furious and wanted a foul, which TV replays suggest was apparent, but Attwell was having none of it.
The Reds should have had an instant response, though, as Tudgay headed over from six yards out after an enticing delivery from Scott Golbourne.
Barnsley started the second half strongly with Craig Davies forcing a low save out of Kirkland, who parried a free-kick before Miguel Llera cleared with a red shirt ready to pounce.
That all changed in the final 10 minutes as former Wednesday striker Tudgay headed straight at Kirkland, Marlon Harewood had an effort blocked and then Tudgay again saw a header cleared off the line by David Prutton as Barnsley threw every forward in search of a leveller.