The Cesena striker had scored twice as Bosnia fought back from two down en route to a penalty-shootout victory over Denmark in the semi-final on Friday.
And he repeated the feat at the Suita City Stadium on Tuesday, scoring in each half after Hiroshi Kiyotake had given the home side a deserved lead just prior to the half-hour.
Bosnia's response was almost immediate, however, with Djuric converting from close range, and the imposing forward netted the winner midway through the second period.
Japan - who had thumped Bulgaria 7-2 in the other semi - made a bright start, Takashi Usami forcing a save out of Bosnia goalkeeper Ibrahim Sehic, who then did superbly to tip Kiyotake's rasping drive onto the crossbar in the 15th minute.
The hosts continued to dominate and their superiority was rewarded in the 28th minute when Usami embarked on a driving run down the left and cut the ball back for Kiyotake, who swept home off the underside off the crossbar.
But the lead lasted just 60 seconds as Armin Hodzic's header was saved by Shusaku Nishikawa and Djuric smashed home the rebound.
Against the run of play, Bosnia almost went into the interval in front as, with the last action of the half, captain Haris Medunjanin crashed a curling 30-yard free-kick off the bar.
Following an open first half, the early exchanges of the second period were less eventful, until Djuric struck again to silence the home crowd once more.
Substitute Miroslav Stefanovic cut in from the right-hand side and slipped a clever ball through to the forward, who slotted low beyond the onrushing Nishikawa.
Earlier on Tuesday at the same venue, Denmark had claimed third place, thrashing Bulgaria 4-0 with Tottenham midfielder Christian Eriksen netting a 10-minute hat-trick in the second half.