Over 1000 Rovers fans saw star striker Jordan Rhodes settle the Huish Park encounter, scoring the only goal of the game just before the hour mark.
It was a match that Rovers should have wrapped up long before Rhodes' strike, the first half alone saw the visitors have a dozen efforts at goal.
But in the end it only needed one to count for Rovers to come away with all three points.
"It is a tough place to come and a long way to come," said Bowyer.
"We had a fantastic following from our supporters, it was an unbelievable effort. We said to the players that the least we could do was match the effort that the supporters have made and I thought our players did that and more.
"I thought we played some really good stuff in the first half and I don't think anybody could have had any complaints had we gone in at the break three or four up.
"If anything we were critical at half time with the fact that we weren't ruthless enough.
"You are always wary of the fact that a team is going to have a spell in the game and Yeovil did that, they hit the post and they've hit the bar but I think overall we thoroughly deserved the win."
Rovers are back in action this Boxing Day when Sheffield Wednesday are the visitors to Ewood Park.
Tickets are currently on open sale with prices from £19 for Adults, £12 Seniors and £7 Juniors. Book online today at www.onerovers.co.uk
and collect your tickets from the Blackburn End collection point at the end of the game.