Pitman finished confidently from close range after goalkeeper Simon Royce had spilled James Henry's testing long-range strike.
Despite the one goal margin on another day it could well have ended 5-5 as both sides enjoyed a number of chances throughout.
The entertainment began on 14 minutes as Warren Cummings swept down the left for Bournemouth and picked out Scott Golbourne at the far post.
The on-loan Reading defender connected first time with a well-executed half-volley, but Royce was athletic enough to tip over.
Gillingham then managed to find some rhythm in midfield and constructed a tidy move which led to captain Andrew Crofts clipping the outside of the post when placing a right-foot effort from outside the area.
The lively Henry was causing problems for a Gills' defence missing the experience Efe Sodje and Ian Cox and the winger caused mayhem in the penalty area just after the half-hour mark with a well taken free kick.
The ball was initially cleared only for Danny Hollands to play it back into the danger zone.
First Sam Vokes saw his attempt blocked by Stuart Thurgood and then the Gills midfielder saved again as Pitman struck the rebound.
Two minutes later though Bournemouth had their crucial goal as Pitman produced a real striker's finish to send his side in at half-time in a jubilant mood.
An equally frantic second half saw Hollands strike the face of the post as he smashed one with the outside of his left foot on 56 minutes.
Gillingham then were unlucky not to draw level as Chris Dickson was denied by Gareth Stewart after bundling his way through only to be given a second bite, but have his cheeky backheel was saved off the line by Jason Pearce.
There was still time for Pitman to strike a post as nerves frayed inside Dean Court, but fortunately for Kevin Bond's side they hung on to lift themselves off the bottom of League One ahead of a busy Christmas period.