Man of the match Anderson de Silva scored the winner two minutes before half-time after Damien Delaney had earlier cancelled out Daniel Bogdanovic's opener.
Barnsley then went on to dominate the second half as De Silva and his midfield partners Hugo Colace and Andranik Teymourian ran QPR ragged, preventing the visitors from putting Heinz Muller's goal under any real danger.
"It was a good performance and I thought we thoroughly deserved the win," Davey said. "There was only one team in it in the second half and we were winning every challenge and gave them everything they could handle."
The Tykes started the stronger side as Colace and De Silva quickly took a stranglehold on midfield, and they got their reward in the 26th minute when Bogdanovic headed in Michael Mifsud's cross for his second goal in Barnsley colours.
QPR had struggled to create much at the other end, with Dexter Blackstock wasting the two chances that Wayne Routledge had managed to set up.
However, they drew level in the 35th minute as Delaney got up to head Matteo Alberti's cross in at the near post.
The Tykes got back in front as De Silva rifled in a loose ball following a set-piece.
After the break, the Tykes remained very much on top and continued to press QPR back inside their own half, although they failed to create too many more clear chances.
Davey had put the emphasis on results ahead of performances earlier this week, but got both as Barnsley made it seven points from the last nine available.
"It's always a bonus to get a good performance as well but we've got three points on the board and a little run going to get seven from nine and that's the main thing," he said.
Davey piled praise on his midfielders for the way they kept Rangers out of the game in the second half.
"You've got Anderson who was man of the match and Hugo and Andranik winning everything," he said.
"I'd back my midfielders against anyone in the division on their day. They're as good as anybody and we just have to make sure they are on their day more often than not. Today they were terrific. They won the battle and we won the game."
Davey was forced into a number of changes to his side, not least with Darren Moore and Jamal Campbell-Ryce suspended, but got a great response from the players he brought in as Adam Hammill impressed in his first start and Dennis Souza handled Blackstock well.
That will give Davey a selection dilemma going to Cardiff on Tuesday night, but not one he is concerned about.
"It's a nice problem to have," he said. "We've got seven points from nine and we can build on that."
While Barnsley have hit a rich vein of form to pull away from trouble, QPR are watching their own goals slip away as failure to win in their last four games has seen them drop away from the play-off race.
Paulo Sousa was disappointed with the result but praised his player's efforts and insisted his targets remain attainable this season.
"It's always disappointing when you want the three points but I'm glad because my players showed a lot of effort to win the game," the Portuguese boss said.
"I said when I first came here that my ambitions were to create a solid base for next season and we are still doing that.
"When you get very close to the play-offs obviously you start to the think about the play-offs, but if you look at the results today a lot of our immediate rivals also dropped points.
"When you see that Nottingham Forest win at Reading you can still believe it's possible."