Second-half finishes from Carlos Vinicius and substitute Mitrovic inflicted a club-record 24th defeat of the season on the division's bottom club to leave them eight points from safety with just two fixtures remaining.
Prime Minister Rishi Sunak - a Saints fan - was among those in attendance on the south coast as the hosts' 11-season stay in the top flight ended in tame fashion.
He witnessed a team lacking confidence, ideas and urgency produce another feeble performance of a miserable campaign featuring three managers and just two home league wins.
Vinicius broke the deadlock in the 48th minute, before Mitrovic, who was handed the lengthy suspension for grabbing referee Chris Kavanagh in his side's FA Cup loss at Manchester United on March 19, condemned Saints to the Sky Bet Championship by heading home his 13th goal of the season.
Boos and chants of “you're not fit to wear the shirt” from home supporters greeted the full-time whistle.
Southampton began the day in the perilous position of needing to win each of their final three fixtures to stand any chance of survival following Monday's damaging 4-3 loss at fellow strugglers Nottingham Forest.
Pockets of empty red seats suggested plenty of Saints fans were already resigned to the club's fate, albeit the reduced crowd was boosted slightly by the presence of Southampton-born politician Sunak.
Unchanged Fulham dominated possession from the first whistle but created little in a forgettable opening period of few chances.
Brazilian forward Vinicius saw a close-range effort blocked for the away side, moments after recalled Saints striker Paul Onuachu fired tamely at Bernd Leno from range following a mistake from Issa Diop.
Fulham then had passionate penalty appeals waved away after Harry Wilson’s inswinging cross struck the arm of Southampton defender Lyanco, prompting visiting players to surround referee Thomas Bramall at the next break in play.
Willian came closest to a first-half breakthrough when his 41st-minute volley was headed off the line by Lyanco following fine work from Wilson and Harrison Reed's ball across the box.
A dismal contest desperately requiring a goal burst into life immediately after the restart. Carlos Alcaraz momentarily thought he had fired Southampton ahead, only for his confident, slotted finish to be flagged offside, before Fulham quickly compounded that disappointment to suck the life out of home supporters.
Vinicius claimed the simple opener, tapping home unmarked from close range after the industrious Reed diverted the ball across goal with a crunching, sliding challenge on Lyanco.
The party mood among the away end was heightened by the long-awaited return of Mitrovic 25 minutes from time, with a host of Serbia flags unfurled on the terraces. And the Cottagers' top scorer wasted little time in reintroducing himself.
The lively Wilson was once again Southampton's tormentor-in-chief, producing a pinpoint cross from the right for Mitrovic to stoop and nod beyond goalkeeper Alex McCarthy.
Victory for Fulham was a club-record 15th of a Premier League campaign and a first away to Southampton since 1935 to lift them to ninth place.
Beleaguered Saints, meanwhile, are left to contemplate a first season in the second tier since 2011-12 and, following games against Brighton and Liverpool, an uncertain summer of transition.
Additional reporting by PA.