Cherries substitute Matt Tubbs cancelled out Billy Paynter's opener for Doncaster when he latched on to Steve Fletcher's header to lob over visiting goalkeeper Neil Sullivan.
With the south-coast club pushing for a late winner to get their promotion bid back on track, Doncaster broke from the back with the ball eventually falling to teenager James Husband, who volleyed home the winner from a tight angle.
Bournemouth were centimetres away from grabbing a stoppage-time equaliser when Brett Pitman's header cannoned back off the post.
After watching his side fall to their fifth straight defeat, Howe said: "I thought we deserved to win.
"It is the story of our recent results. The ball just isn't bouncing for us at the moment, but I was really pleased with the performance.
"It is not a nice feeling, but we will role our sleeves up.
"We have got to bounce back there are massive games coming up and we can still achieve something this season.
"We may look back on this as a turning point for us."