The Cherries snatched the winning goal after 22 minutes as Lewis Grabban crossed from the left and Brett Pitman swept in from six yards.
Grabban and Pitman both had chances to double the lead, but Oldham did not threaten until Jordan Obita's shot was saved on the hour-mark.
The home side wasted a 70th-minute penalty when Grabban was penalised for handball and Jose Baxter audaciously chipped his spot-kick down the centre of goal. Bournemouth keeper Ryan Allsop had already dived to his right, but managed to reach out a hand and claw the ball down into his arms.
Howe said: "It's all about results at this stage of the season. We needed to win and we did it with a dogged, disciplined performance.
"The opposition didn't help the spectacle of the game because they were very direct and played a lot of long balls, but our back four repelled that well.
"This is a good group of lads who work extremely hard and aren't arrogant enough to think they can't improve.
"We are working on being more resolute and credit to the players for helping us to achieve that.
"It always helps when you've got an attacking player who is scoring goals and Brett Pitman is doing that at the moment. He is a big-game player.
"We got a good result from a difficult game and we have to be ready for the ups and down that will come in the last few weeks of the season."