The Serbian striker won and scored a second-half penalty as Scott Parker's side chalked up back-to-back victories and the sort of performance it seemed incapable of delivering during a nine-game losing streak between February and April.
The result spoiled Bournemouth manager Eddie Howe's celebrations as he took charge of his 500th game, and he saw Callum Wilson and Ryan Fraser miss big chances just a week after they both scored in a 5-0 mauling of Brighton and Hove Albion.
Bournemouth has three more games to stake its claim for a place in the top half of the Premier League table but on this showing it looks unlikely to match its ninth-placed finish from two seasons ago.
Fraser got in behind the Fulham defence and crossed to the feet of Wilson on the edge of the six-yard box but the striker leant back and blazed over the crossbar with his first-time shot.
Mitrovic volleyed over the top at the other end before Sergio Rico made a superb save, getting down to parry Fraser's drive away after the winger's mazy dribble
Junior Stanislas went down clutching his knee after taking a free-kick and was replaced by Jack Simpson, while the best Fulham could muster before the interval was a Denis Odoi header from close range that Artur Boruc got down well to save.
Ryan Babel headed over the crossbar from 10 yards as Fulham pressed early in the second half and it made the breakthrough after Simpson was judged to have fouled Mitrovic in the box.
Mitrovic buried the penalty in the bottom left corner and Fulham continued to attack, Sessegnon twice testing Boruc before Fraser was denied in a one-on-one with Rico having latched onto David Brooks's defence-splitting pass.
Rico twice denied Wilson at close range as Bournemouth sought an equaliser that failed to materialise and Boruc made a superb diving save from Joe Bryan's angled drive to spare his side further blushes.