New head coach Gerhard Struber described his side's 3-1 victory at home to Hull as the "first small step in the right direction".
Goals from Alex Mowatt and Mike Bahre in either half put the home side in control before Keane Lewis-Potter reduced the arrears, but Barnsley held on to record their first win since the opening day of the season with Conor Chaplin adding a third in stoppage time.
Struber said: "It was a very important game. The last days were very difficult for the mindset for my players. We have a clear plan for what we want and we have a very good conviction and self-confidence.
"I speak a lot in the last days with my players and I think the right plan on the field and the right character was the key for the result and the good performance.
"I am very proud of my boys and I am happy. I am here for 10 days and this is our first small step in the right direction.
"The support from the fans is always important but now very important and I'm happy with our fans.
"The next week we have a long week and I hope the next game away we have a top performance again.
"Alex (Mowatt) is a leader and a very important player for my team. He can score and he can work very hard on the field. He gives the other players a good feeling."
The hosts took the lead midway through the first half when Bahre laid the ball off to Mowatt who produced a measured shot to beat keeper George Long from the edge of the area.
Hull's best chance of the half fell to Jarrod Bowen, whose low shot went a fraction wide of Sami Radlinger's right-hand post.
Barnsley established a two-goal cushion in the 75th minute when Mowatt slipped a great ball through to Bahre who slotted confidently past Long from inside the area.
The visitors pulled a goal back when Kamil Grosicki's cross from the left was headed back across the face of goal by Tom Eaves at the far post and substitute Lewis-Potter was on hand to head in from close range.
Chaplin scored a third goal for Barnsley deep into stoppage time with a thumping drive from the edge of the area.
Hull manager Grant McCann was critical of his team's passing.
He said: "It's disappointing because we didn't play very well at. We couldn't pass the ball from A to B.
"Credit to Barnsley because they pressed us well, but we didn't show any calmness, any authority or braveness in possession.
"I'm just angry with us in possession more than anything else because I think we showed on Wednesday night how good we are in possession. Today we didn't show anywhere near that.
"We had 11 performing on Wednesday night and today we had zero – it's as simple as that.
"It's the Championship and if you don't perform you get beat – I've said it from day one. Today we didn't perform. We were just way off in terms of what we wanted them to do.
"We've been on a decent run and we've had a tough week, going to Middlesbrough and going to Barnsley and at home to Preston.
"We've taken four points out of it and could possibly have had six because I thought we played well in the second half at Middlesbrough."
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