The Owls ended a seven-game losing streak thanks to Chris O'Grady's first-half strike which was shrouded in controversy after Gary Madine appeared to foul Barnsley goalkeeper Luke Steele in the build-up.
Jones, who has been clinging on to his job in recent weeks in the midst of his side's dire run, has pointed to a run of decisions going against Wednesday in recent weeks and was happy to take the good fortune, though was still not happy with referee Stuart Attwell's performance.
"It was ugly but well earned," he said of the win. "We had Lady Luck on our side for a change, but we deserved it because we battled hard.
"Gary has admitted that he has barged the goalkeeper, we have not had that luck but today it was our time.
"We got the break today, last week we battered Bristol City and didn't get the break.
"But I thought the referee had an absolute shocker to be fair. Everything after that went against us and he struggled to keep control."