It took just one minute for Antoine Semenyo to erupt the Vitality Stadium as he calmly cut inside and slotted his shot into Bernd Leno’s net.
The Cherries came into the game without a league win for two months, picking up just two points in their last six games.
Fulham on the other hand, headed into the game off the back of beating league leaders Liverpool 3-2 at home.
Andoni Iraola made just one change from their 2-2 draw against West Ham with Marcos Senesi coming in for Illia Zabarnyi.
The Cherries started with their fast paced intensity, winning the ball back quickly which gave them multiple early chances.
Semenyo took advantage of their first chance as he stole the ball from Antonee Robinson before cutting inside and curling the ball into the corner of the Fulham goal.
Evanilson was on the end of a great Bournemouth move 17 minutes in as his outstretched boot fired the ball too high and hit the crossbar from just five yards.
Muniz then had Fulham’s best chance of the first half as a mix up between Senesi and Huijsen allowed him through on goal, only for him to drag his attempt wide of the post.
As the second half started Illia Zabarnyi came on to replace Marcos Senesi and the game picked up just where it left off, with an end to end game giving both teams their fair share of chances.
Kepa was called upon often in the second half as Fulham seemed to take control of the attacking chances however the Spaniard did well to keep them at bay and ended with seven saves.
A VAR check in the 80th minute did not award Bournemouth a penalty as Evanilson seemed to be brought down by Bernd Leno in the box.
The win moves the Cherries up to eighth in the league with the possibility of European football in their sights.
Bournemouth now have four days to prepare before travelling to the capital to take on an in-form Crystal Palace side on Saturday.