Gilbert made the decisive break seven kilometres from the line to cross the line alone several seconds ahead of Slovenian Grega Bole and Belgian Ben Hermans.
It is the fifteenth success this season for Gilbert who holds a six-second lead on Norway's Edvald Boasson Hagen with Scotland's David Millar 14 seconds off the pace.
"It was a very difficult final because there was a lot of head wind in the final five kilometres. And then it was a bit like Omega Pharma against the rest. Thankfully I know the route very well. It's obviously an advantage," explained the world number two.
Friday's fourth stage is a 14.7km time-trial at Roermond in the Netherlands.
"It will be very complicated against the individual specialists in particular against Edvald Boasson Hagen," warned Gilbert.
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