Alex Mowatt's assured finish from the edge of the penalty area put Barnsley ahead at Oakwell
Head coach Gerhard Struber said his struggling Barnsley side took their "first small step in the right direction" with victory against Hull City.
Victory was the Tykes' first since the opening day of the season and first under the Austrian.
Barnsley captain Alex Mowatt fired home from the edge of the box to put the home side ahead midway through the first half.
Mowatt was also involved in the second as he slipped a pass through to Mike Bahre to double the lead.
Keane Lewis-Potter headed one back for Hull, but Conor Chaplin added a third in injury time to end Barnsley's 18-match winless run.
"It was a very important game," 42-year-old Struber said. "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's second goal of the season put Barnsley ahead at Oakwell
Barnsley remain bottom of the Championship but are now five points from safety.
Struber had lost his first two games in charge, but watched his side start well in the opening home match of his tenure.
Cauley Woodrow had gone close before Mowatt guided in a fine left-footed strike for his second goal of the season.
The Tykes had a let-off just before half-time when Hull's top-scorer Jarrod Bowen raced clear, only to drag his shot wide.
Chaplin thought he had doubled the lead early in the second period but was flagged for offside, before Hull's Jackson Irvine went close.
Barnsley's second goal finally arrived with 15 minutes to go, when Bahre finished past George Long.
Lewis-Potter's header made it a nervy finale but Chaplin struck in the 95th minute as Barnsley tasted victory for the first time since August.
Hull City boss Grant McCann told BBC Radio Humberside his side "weren't good enough" against the division's bottom side.
"We couldn't pass the ball from A to B, we were lacklustre," McCann said.
"Everything was a bit rushed and we had no real calmness. Overall I'm really frustrated.
"We've been on a decent run and today we've come back down to earth. That's the Championship, if you don't perform you will get beat.
"I'm so disappointed for the travelling fans because apart from young Keane's goal we have given them absolutely nothing to shout about."
