Hawley made the most of an unexpected opportunity after a horrific defensive blunder by Bournemouth's Irish centre-half Shaun Maher.
Maher allowed a goal-kick by Carlisle goalkeeper Keiren Westwood to drift over his head in the centre-circle to give Hawley a clear run on goal.
Maher managed to catch up with the speedy Carlisle striker only to bring him tumbling down to concede an unnecessary spot-kick.
Maher was booked for his troubles and was fortunate to escape a red card and from the spot Hawley sent goalkeeper Neil Moss the wrong way with a confident kick.
Carlisle spent much of the rest of the match on the defensive and did not create a clear-cut chance of their own for the remainder of the match at Dean Court.
But with Peter Murphy and veteran Kevin Gray in fine form, Westwood had little to do and it was not until the second half that he was pressed into serious action.
Bournemouth had plenty of possession but had nothing to show for it despite plenty of hard work and some neat build-up play.
New manager Kevin Bond is still looking for his first league win at the Bournemouth helm because it is eleven League Two matches since the Cherries last tasted victory – way back on September 11.
Once Carlisle had gone ahead, Bournemouth strove valiantly to get level with Chris Billy almost conceding an own goal and Maher hooking wide from twelve yards as he looked to make amends in the best possible way.
Steve Fletcher knew little about a mis-hit effort which cannoned wide from six yards and the hard-working Danny Hollands shot across the face of the goal with a fierce left-foot effort that drifted just wide.
Carlisle managed to get forward before the break with Kevin Gall seeing an effort blocked by the feet of Moss while Hawley lifted a shot over the bar when Gall found him clear.
It was the same story in the second half and Maher again came close to redeeming himself with a powerful header from a Steven Foley-Sheridan free-kick which Westwood pushed away at full stretch diving to his right.
The ball looked as if it should end up in the Carlisle net but Murphy somehow got back to clear from the line.
Westwood also made timely stops from Foley-Sheridan and Hollands only to mar an excellent afternoon's work by getting himself booked in the 62nd minute for time wasting according to the referee.