The Cherries had not won in seven games going into the clash, and could have seen that run extended as Lee Hughes twice headed over the bar for the Magpies in the opening period.
Stephen Purches shot wide for the visitors, while Danny Ings showed a sign of things to come with an effort that Stuart Nelson saved.
Bournemouth took the lead in the 67th minute when Liam Feeney sent over a cross from the right and Anton Robinson sent a thumping header home.
Ten minutes later, with County pushing men forward to try and level, Ings doubled the lead and secured the points with a piece of individual skill.
After receiving the ball from Harry Arter, he powered his way through a shell-shocked Notts defence and finished past an equally statuesque Nelson.