The Serbs squandered their first chance after 12 minutes when Milos Ninkovic found himself with time and space but blasted Milos Krasic's inch-perfect cross over the bar.
Mueller and Klose always looked threatening for Germany but the latter's frustrations mounted after he missed chances and had a goal ruled out for offside on the half-hour mark.
The game was turned upside down seven minutes later when the German forward was given his marching orders after receiving a second booking for bringing down Milos Krasic.
With the Germans stunned, Serbia took full advantage and snatched the lead a minute later with a superb team effort that culminated in Jovanovic's close-range strike.
Zdravko Kuzmanovic slid the ball into the path of Krasic, who delivered a delightful cross that was headed to the unmarked Jovanovic, who chested down and converted on the turn.
Germany's Miroslav Klose is involved in an aerial duel with Serbia's Dejan Stankovic (left)
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