Barnsley stunned the home side when Chris Dagnall opened the scoring, but the sending off of Jean-Yves M'Voto changed the game. Tom Cairney responding immediately, scoring from the resulting free-kick and from that point on there was only going to be one winner.
Jordan Rhodes got his season up and running with a first-half brace, whilst there was also first goals of the campaign for man-of-the-match Josh King and Todd Kane.
Not even a Tomas Cywka strike to make it 5-2 could take the gloss off a thoroughly enjoyable afternoon.
"It was important that we got the first win so to do it at home in front of our home fans was pleasing," Bowyer told Radio Rovers.
"The sending off changes the game but you then have to play against ten men and I thought we played against it well and scored some very good goals. It was a pleasing afternoon for us.
"I thought we started well but went a goal down again which is something that we've got to address. But I thought the lads responded well.
"It was a fantastic free-kick from Tom, he's a fantastic technician, he's got great ability and I think he showed what he was capable of from set-plays, he adds another dimension to our play.
"Then you saw the confidence come back with the lads with everybody wanting the ball and we scored some great goals.
"It is important that we got that first win, we've just got to make sure that we work extremely hard for next week."
Rovers are back in action against Bolton Wanderers next Saturday. Tickets are on open sale.
Tickets are priced from £19 Adults, £12 Seniors and £7 Juniors. Book online today at www.onerovers.co.uk