Michel Bastos marked his Schalke debut with a goal, but Felix Klaus levelled before Djurdjic scored a dramatic late winner for Mike Buskens' men.
The win will be particularly sweet for former Schalke player and coach Buskens and striker Gerald Asamoah, who remains a terrace hero in Gelsenkirchen.
Schalke quickly made it clear who the man of the house was, but their superior possession rarely led to clear-cut chances.
Roman Neustadter was the first to test Furth goalkeeper Wolfgang Hesl with a header as the Bavarians employed their familiar defensive, and destructive, tactics.
Matthias Zimmermann made a clearance off the line to deny Jermaine Jones an opening goal in the 22nd minute before Milorad Pekovic followed suit to deny Neustadter.
Schalke took a deserved lead just two minutes into the second half with Bastos showing why the Royal Blues wanted him so much with a curling, unstoppable shot from the edge of the penalty area.
Yet their lead lasted only five minutes. Djurdjic pulled the ball back from the goal line on a rare Furth attack, and Klaus was left totally unmarked for one of his easiest Bundesliga goals to bring the Bavarians level.
Furth then abandoned their defensive style and started to cause problems of their own.
Schalke continued to look the more dangerous, though, and had a third effort cleared off the line in the 68th minute when Benedikt Howedes' header was swept away by Zimmermann.
Raffael hit the post as the Royal Blues tried everything they could to get a winner.
But the Arena AufSchalke was stunned to silence in the second minute of stoppage time when Djurdjic looped in a header after Timo Hildebrand could only parry Azemi's shot, denting Schalke's Champions League hopes.