The powerful attacker scored twice in 12 minutes to send the Reds into their second A-League grand final - the other, a loss in 2007.
Djite broke the deadlock with a stunner in the 48th minute: after Marcelo Carrusca sliced through Melbourne's defence and laid off, Djite, from about 16 metres, launched a sweet right-footer that smacked into the side netting.
And in the 60th minute, Djite added another after Bruce Kamau, whose speed and skill bothered City all night, was brought down in the box.
The contact from Melbourne defender Jack Clisby appeared marginal, but Djite assuredly slotted the penalty with a low-left blast to delight the sell-out 15,489 Adelaide crowd.
City's Fitzgerald then caused some home-town jitters with a clinical right-footed goal from 10 metres out to revive the visitors with 20 minutes remaining.
But their fate was soon sealed: in the 88th minute, from an Adelaide corner, McGowan deflected into the net from close range and, in the last minute, Sanchez added another as United remained on track to claim the double - the Premiers Plate and the Championship trophy.
-AAP