A Jordan Rhodes penalty and Scott Dann's header - both in the first half - were enough for a 2-0 success, and Rovers finished the day a point clear of third-bottom Barnsley with five games to play.
The first of those is at home to Huddersfield on Tuesday, and caretaker manager Bowyer wants his players to focus quickly.
He said: "We can't look any further than Tuesday. As much as we want to enjoy this win, we've got to refocus on preparing properly.
"The situation that we're in now, if we're fourth from bottom on May 4, there will be a lot of happy people. Not for the reasons we should be happy, but because we've stayed in this division.
"I thought the energy we showed and the way they went about it was pleasing.
"We started the game on the front foot and got the penalty that settled us down and gave us confidence. It gave us a boost. Obviously to score right on half time was excellent timing."