The Owls earned the vital points in the South Yorkshire relegation scrap thanks to Madine's first strike since early December, with Reda Johnson's header giving them a two-goal cushion.
They had to endure a nervy ending, though, as Lewis Buxton saw red for two yellows while Jacob Mellis powered home a injury-time consolation for the Reds.
"Gary had a good season last year and he scored a lot of goals," the Wednesday manager said. "He has struggled to adapt at this level but he has worked at it and worked it. There has been a lot said about it, about a falling out. There has never been any problems."
He went on: "Strikers are commodity that everyone wants if they can score goals. It's nice for him to get his goal. If I didn't feel he could score goals he wouldn't be here. We will keep working with him."
Wednesday were second best until Madine's opener, but Jones felt his side were worthy winners in the end, adding: "The second half we took it to them and thoroughly deserved the win in the end. It was all about getting the three points for us. We got in behind them a couple of times in the second half and could have won by more."
Barnsley boss David Flitcroft, who saw his side drop into the bottom three after the loss, was left to rue not being able to take the lead after dominating the first hour.
"We have got to be constructive, the two goals were disappointing, they came when we had momentum," he said. "When you have a foothold you have to make sure you lock that down.
"The second goal has really disappointed me, we had to be brave. At 2-0, the momentum is with Sheffield Wednesday and I didn't want it to turn into a rout. To come here and leave with a 2-1 is the only positive we'll take.
"I have picked these players up before. They are eight more games to look forward to. The pressure on us is to stay in the league, but the pressure is on other teams to get out of it and they are just panicking and we have to take advantage. The players are hurting but when we leave here, we leave proud and in a positive state of mind."
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