The Tykes took a seventh-minute lead on Saturday afternoon and never fell behind despite conceding three times to their visitors from London.
Struber's side have now picked up four points from the last six on offer, after drawing 1-1 with Reading on Wednesday night.
The Austrian coach has now guided the Reds to two wins in their last five league outings, more than they managed in their opening 17 fixtures.
Barnsley are still bottom of the table but are well within reach of the sides above them as Struber now aims to put together a winning run to help the Tykes climb to safety.
“I am very very happy for my team and for every Barnsley fan," he said.
"I think this was a very, very important game for us, to create a good performance and get very important points.
“It was a very difficult week and, in the end, we have four points which is two points too little but my players created together two very good games.
“My players had the winning DNA today which is what we need for our big challenge to stay in the league. I saw the mentality that was not like a relegation team.
“It’s always good when we win, for our self-confidence and our faith.
"Big victories are always good for our soul and for our heart. We are happy today but we have a lot to do to make sure we can consolidate this performance.”
Struber was disappointed to see his side concede three times as Luke Amos struck in either half for the visitors before Ilias Chair added a consolation with the last kick of the game.
But the Barnsley head coach insists that he has plan to improve the Tykes' defensive frailties.
“The reality is we conceded three goals. We have to work very very hard on the training pitch in the next week," said Struber.
"My to do list is long but, step by step, we will get better in our process and I hope next week we will have good performances and get more points.
“We have a free week now and the training will help us to be a more compact team in defence. I have a plan for the next week so that we can do that."
Conor Chaplin scored a hat-trick inside the first 51 minutes before Cauley Woodrow scored from the spot to give the Reds breathing space.
Bambo Diaby completed the scoring as he got on the end of Jacob Brown's low cross to seal the three points for the home side.
“I am very happy with Conor but I am very happy with Cauley Woodrow and my other players," Struber said.
"Every player is very important in our concept and our programme.
"My style is always teamwork but not creating for one or two players. We need every player and every player did a very good job today.”
Mike Bahre was substituted after 32 minutes, with Luke Thomas taking his place, but Struber revealed that decision wasn't influenced by an injury.
He added: “It was a tactical situation. Mike was not so fresh and it was a problem for us.
"Luke played a good game and, for the team, a small correct decision.”