Following the dismissal of Henning Berg, Bowyer led Rovers to their first win in seven games which saw the club move up to 15th.
Goals from Joshua King, Ruben Rochina and Jordan Rhodes secured a comfortable victory that led to the sacking of Barnsley boss Keith Hill.
"It was an important win for us, it has been a tough couple of days," said Bowyer.
"The players were good in training yesterday (Friday) and they have carried it through into the game today (Saturday).
"We worked with them on the shape yesterday and they just got on with the job.
"There was a good feeling in the dressing room at half-time because of the level of performance and I just told them if they wanted this feeling at full-time they had to play the way they played in the first half.
"All the players played well. I don't like singling players out but Rhodes, a Barnsley lad, played well on his return to Barnsley."
- Sports & Recreation
- Jordan Rhodes
- Ruben Rochina