Howe's charges came back from the disappointing home draw against Macclesfield on Saturday to down Ian Hendon's Londoners 3-0 and regain second place in the League Two standings.
Steve Fletcher headed home Liam Feeney's cross just before the hour mark, before Pitman took advantage of some comedy goalkeeping from Bees' Jake Cole to double Cherries' advantage minutes later.
Pitman then slotted home Cherries' third with 15 minutes remaining to leave Howe beaming.
And it was no less than the home side deserved after a first-half performance that had promised much of what was to come during an absorbing clash.
Howe said: I thought we had a number of chances in the first half and we were disappointed to come in level at half-time.
I felt we deserved to be at least two goals in front. In the second half we could have rattled up more, but we were certainly happy with the three.
I wasn't worried at half-time because we looked like scoring at any time.
Brett is a livewire and part of his success is that he doesn't get concerned with missing chances. He just says to himself that he will take the next one.
He won't pass the responsibility on and that is a huge strength to have as a centre forward.
I hope he continues to take that responsibility because I'm only too pleased to let him have it, added Howe.