Philippe Gilbert took the stage win after breaking away from a small lead group with just four kilometres remaining, after three attacks from Vincenzo Nibali - who lay third, just 11 seconds behind Hincapie - had shaken the veteran American and his Discovery Channel team-mates.
The Belgian, who counted on huge local support, appeared to catch Hincapie knapping, and Schumacher attempted to go with him. The German though, was unable to maintain the tempo required to stay clear of the quickening bunch behind.
While Gilbert could not open the required 18 second gap to snatch overall victory himself, he took victory as the Belgian public roared him across the line.
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Behind him, Schumacher launched his sprint on the inside in a bid to pick up the necessary bonus seconds to take him ahead of Hincapie at the top of the standings, but the American remained on his wheel.
Just 75 metres from the line, Schumacher swerved violently - though seemingly unintentionally - away from the barriers, only just managing to right himself, but clipping Hincapie's front wheel and sending him crashing to the tarmac.
The Gerolsteiner man was narrowly edged out by Italian Manuele Mori into third place, though the four second time-bonus awarded meant that he overtook Hincapie by a single second in the standings, sealing overall victory in the tour.
Schumacher afterwards explained "I started the sprint on the inside, and as I was going along, one of the spectators caught my left arm. I almost fell and my bike swerved to the right."
The American, predictably, was unamused. He refused to finish the stage, initially remaining on the ground with a look of disbelief on his face, before walking to the finish area, where he exchanged choice words with Schumacher.
Hincapie is likely to be given the same time as the rest of the group, meaning he would finish as runner-up on the Tour, though that will prove of little consolation.
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