Nicky Southall scored the only goal of a mediocre game just before the hour mark after good work from Andy Barcham. With several of their other rivals dropping points, Gills climbed to sixth while defeat left Bournemouth rooted in the relegation zone.
Mark Stimson's side have an excellent home record this season, but a slow start handed the initiative to the Cherries.
They had the opportunity to move clear of the bottom two with victory and they quickly settled, but despite their dominance, a wild shot from skipper Danny Hollands was the closest they came.
At the other end, Mark Bentley almost gave Gills a lead against the run of play with a firm header which was well saved by Shwan Jalal. His opposite number, Simon Royce, made an equally impressive save two minutes before the break to parry Mark Molesley's well-struck shot.
The game swung decisively in Gillingham's favour with a substitution ten minutes into the second half. Top scorer Simeon Jackson, starting from the bench for the third successive game, immediately caused problems and within three minutes was involved in the only goal of the game.
The Canada striker's cross was long but Barcham chased down the lost cause before spinning his marker on the byline. Drawing the goalkeeper he pulled the ball back to Southall, who threaded a shot from eight yards past several bodies on the line.
Although there were still more than 30 minutes remaining it was the final clear chance. Instead, the game became increasingly bad tempered, with five players booked in the last 20 minutes.
It was far from a classic, but the result was all-important to a Gills side who have so far struggled to maintain a place in the play-offs.