Aleksandar Mitrovic’s second-half penalty gave the 19th-placed Cottagers a first league victory on the road since beating Millwall in the Sky Bet Championship on April 20 last year.
The Serbia international converted from the spot after being brought down by Cherries substitute Jack Simpson to halt a goal drought dating back to January.
Victory at the Vitality Stadium, which spoilt the landmark occasion for Cherries boss Howe, strengthened the hopes of Fulham caretaker boss Scott Parker landing the job on a permanent basis.
After beginning his Craven Cottage tenure with five consecutive defeats, Parker has now guided the west London club to successive league victories for the first time since promotion last May, restoring some pride at the end of a torrid season.
Mid-table Bournemouth initially stuck with the team which thrashed Brighton 5-0 last weekend but manager Howe was forced into a change when right-back Adam Smith withdrew in the warm-up due to injury.
Smith’s makeshift stand-in Junior Stanislas lasted just 23 minutes before limping off to be replaced by academy graduate Simpson, leaving the Cherries with a backline comprising four centre-backs.
The hosts had begun brightly in the south-coast sunshine and Fulham goalkeeper Sergio Rico had to be alert to smother Callum Wilson’s early close-range header.
Wilson’s unmarked strike partner Joshua King then somehow side-footed over from only six yards out after being picked out by Ryan Fraser.
Brilliant work from Fraser on the left as his ball finds King in the box, but the striker can't direct it on target. #BOUFUL 🍒 0-0 ⚪
— AFC Bournemouth (@afcbournemouth) April 20, 2019
Championship-bound Fulham, buoyed by registering their first win under Parker at home to Everton last weekend, grew into the game.
Calum Chambers’ goal-bound header was nodded off the line by Nathan Ake, before captain Mitrovic wastefully volleyed over moments later having found space inside the box.
The loss of Stanislas seemed to disrupt the hosts and they again survived a scare eight minutes before the break when goalkeeper Artur Boruc got down well to repel Denis Odoi’s header from a Ryan Babel corner.
Fulham continued to threaten early in the second period and went ahead in the 53rd minute as Mitrovic made up for his earlier miss by claiming his 11th league goal of the campaign and first in 10 top-flight outings.
After being brought down in the box by a clumsy swipe from Simpson, the former Newcastle man picked himself up to calmly send Boruc the wrong way from 12 yards.
The opening goal prompted chants of “1-0 to the Championship” from a sold-out away end bathed in sunshine and they almost had more to celebrate soon after as Ryan Sessegnon was twice denied by Boruc.
Bournemouth winger David Brooks, shortlisted for the Professional Footballers’ Association Young Player of the Year award earlier on Saturday, then broke away and slipped in Fraser at the other end but Rico superbly smothered the winger’s effort.
Spaniard Rico, on loan from Sevilla, was enjoying a fine afternoon and reacted well to again deny Wilson, with Cherries substitute Dominic Solanke unable to capitalise on the rebound.
The home supporters were growing increasingly frustrated and angrily called for a red card when Mitrovic barged into Ake, a challenge referee David Coote deemed worthy of only a booking.
Fulham were forced back for much of the closing stages but, despite a Brooks cross landing on top of the crossbar and six minutes of injury-time, the hosts ran out of ideas and were unable to salvage a draw.