Wrexham's 18-league match unbeaten run ended in front of a disappointed home crowd at the Racecourse.
Disenchanted fans trooped away before then end, wondering how the side that had won 3–2 at Sheffield Wednesday earlier in the week could play so poorly and hardly look like scoring.
It all went wrong when bad defending cost an early goal. Warren Cummings crossed from the right, Carl Fletcher headed down and Stephen Purches scored with a long-range shot that bobbled as it crossed the line with Andy Dibble unable to scramble across his goal.
Dibble kept the score down with a good save from Marcus Browning but the keeper had only one more save to make, turning James Hayter's angled shot past the back post at the expense of a corner.
Wrexham also missed the impact of the suspended centre-back Brian Carey, although his 18-year-old deputy Craig Morgan settled and played well following the disastrous early goal.
Stephen Thomas had a shot headed off the Bournemouth line and set up an opening for Hector Sam who hit high and wide into the visitors' stand.
Neil Moss saved two free-kicks that Thomas curled straight into his body from the edge of the area and when Carlos Edwards nearly set up another chance neither Chris Llewellyn nor Paul Barrett could get a touch as it flashed across the goal.
Bournemouth manager Sean O'Driscoll thought they might have done better after a good start. He said: "Once we were in front I think we panicked a touch and took our foot off the pedal. I was pleased to get the lads in at half time and from there on we had more control of the game." Wrexham boss Denis Smith was sad to see the end of their successful run but he had been handicapped with important players out.
"We have taken ten points from the first five games and if we carry on like that we will do okay. We were a goal down before we started to play but we were better in the second half."