It was Rodrigo Muniz's afternoon as the young Brazilian striker netted twice to help Marco Silva's side to all three points on home soil.
Bobby Decordova-Reid got the ball rolling for the Cottagers, before Muniz added a second before half-time.
Bournemouth briefly threatened a comeback though, when Marcos Senesi's fine footwork allowed him to half the deficit early in the second period.
However, barely 60 seconds later and Fulham restored their two-goal lead, with Willian picking out his Brazilian compatriot superbly to put the hosts back in the ascendancy.
For Fulham, it is just a second win in 14 meetings with Bournemouth, as the away side suffer their first defeat at this stadium in nine visits.
Andoni Iraola's men fall one place below Fulham into 13th, but remain a comfortable eight points clear of the relegation zone.
Bournemouth were chasing the game virtually from outset, as Decordova-Reid capitalised on some slack defending to give the home side the lead inside five minutes.
Despite some good hold up play by Muniz, it was ultimately a very costly slip by Lewis Cook that presented the opportunity on a plate for Decordova-Reid, who fired beyond Neto from close range.
Neto was kept busy in the Bournemouth goal, needing to be alert to keep out both Willian and Antonee Robinson inside the opening half-hour, as Luis Sinisterra also saw two promising chances go begging at the other end.
Fulham would then go on to double their lead with just 10 minutes remaining of the first half, as Willian's cross was nodded down by Decordova-Reid and Muniz nipped in ahead of Neto and Illia Zabarnyi to prod home.
Bournemouth could have pulled one back soon after when Marcus Tavernier dragged an effort wide, but they would not have to wait long into the second half for that important goal to get them back in the game.
After Dominic Solanke kept the chance alive from a deep corner, Senesi showed excellent footwork to flick the ball over his own head before volleying beyond Bernd Leno in the Fulham goal.
However, it took less than a minute for Fulham to restore their two-goal lead, as Willian was given too much space to cross on the left, and picked out Muniz, who was able to fire home emphatically from a matter of yards to make it 3-1.
With two goals required, Bournemouth then took control of proceedings, as Iraola introduced Enes Unal up front for a debut alongside Solanke in a two-pronged attack.
The Turk was lively, and arguably should have notched a debut goal when Senesi's drilled cross flashed beyond him before being put into touch by Tim Ream inside the six-yard box.
The Cherries were ultimately wasteful in the final half-hour though, as Fulham were able to hold on for a relatively comfortable victory on home turf.
Having now taken 22 of their 29 points this season at Craven Cottage, Fulham will be confident heading into another home clash next weekend when Aston Villa travel to West London.
Bournemouth are on the road again, but have a very lengthy trip to the North East to face Newcastle United, as they look to recover from this weekend's defeat.