Bournemouth went further behind in the 39th minute after an amazing blunder by goalkeeper Asmir Begovic. Zigor Aranalde pumped a 40-yard free kick towards the Bournemouth goal and, instead of turning the ball over the bar, young Canadian Begovic succeeded only in pushing it onto the line where Garner was waiting.
Bournemouth improved after the break and they were given a lifeline in the 54th minute when Keiren Westwood did well to block a shot from Max Gradel but the rebound fell for Jo Kuffour who snapped up the rebound.
Bournemouth were undone again in the 66th minute when the hapless Telfer again got in the way of an attempted clearance and the rebound fell into the path of Joe Anyinsah who shot home from the edge of the area.
Nothing went right for Bournemouth and they twice struck the woodwork in desperate attempts to get back into the match. Westwood dived full-length to turn a header from Lee Bradbury against the bar and then, with five minutes remaining, a curling shot from substitute Sam Vokes also struck the bar.
Westwood also made good saves from Bradbury and Danny Hollands, but there was no way back for Bournemouth. In the first half Carlisle were by far the better side and Simon Hackney twice went close.
Danny Graham mis-hit in front of an open goal and Portsmouth-loanee Begovic partly made up for his mistake by going to his right to turn away a 20-yard effort from Anyinsah.