The Bees were unable to provide a tonic for sick boss Edgar Davids as Jacques Maghoma scored the only goal of the game from the penalty spot after just four minutes to secure a fifth successive win for Rowett's side at the Pirelli Stadium.
But it was the visitors who often produced the better brand of football on a tricky surface, only to be let down by a lack of cutting edge.
Rowett said: "We defended and we saw the game out. Barnet always seem to get a result here so I'm just pleased we've won the game - that's all that matters to me really.
"Some people could have argued we've not done much wrong at home so why change it, but I just felt as though I wanted to get both Ian and Stuart in the side.
"I think they both showed what they give us. Sharpsey has got the experience and he goes and wins headers and Tomlinson is a big presence in the penalty area."
Rowett acknowledged a below-par display by his side but insisted the result was all-important.
"It was by no means the best we've played all season. It was a scrappy sort of game and we just couldn't retain the ball enough," said Rowett. "I would like to see us play better, of course, but it's another home win and that's what is keeping us in the play-offs.
"I set a target in my mind of 45 points from the first 30 games and we've done that with one to spare. Anything we can get on Tuesday (at Oxford) will be a real bonus."