Matt Ritchie had to be withdrawn after 33 minutes with his replacement Ryan Fraser then having to come off midway through the second half, while Harry Arter was substituted in the final minute of the 1-0 win.
The Cherries ended a run of five straight defeats thanks to Brett Pitman's 38th-minute penalty.
The result is a timely boost for Bournemouth's promotion hopes as, although they remain seventh and outside the play-offs, they now lie just four points behind second-placed Sheffield United.
Manager Eddie Howe said: "It didn't all go according to plan with Matt Ritchie, Harry Arter and Ryan Fraser all getting injured.
"In terms of the playing side I thought we were excellent in the first half, showing some of the best football we've played in a few weeks.
"I was really pleased with how the lads were composed as we moved the ball well on a difficult surface against a difficult team.
"In the second half, I think because of a couple of changes we were forced to make, we lost control of the game but defended very well. There's been a few question marks about our defending in recent weeks but the lads proved a point.
"Individually, they are top players and I rate them very highly. Collectively, as a group, we haven't performed as well as we can do defensively in the last few games so full credit to them for the response here."