The 26-year-old Bora rider held off Norway's Alexander Kristoff and German pair John Degenkolb and Marcel Kittel in the dash to the line at the end of the 190km stage from Chablis to Chalon-sur-Saone.
"It's my first victory at this level and I'm very proud," said Bennett, whose father Michael was a professional footballer.
"As a sprinter I think I've got the speed but I don't have the greatest amount of power," he added.
"Usually I'm more at home on a lumpy stage (where pure sprinters might struggle)."
France's Arnaud Demare came in sixth and held on to the leader's yellow jersey.
A breakaway group comprising French pair Romain Combaud and Pierre Latour, alongside American Ben King, came agonisingly close to battling out the victory.
But having escaped inside the first kilometre, they were caught in the very last one by a charging peloton led by the sprinters' teams.
Wednesday's fourth stage is a 14.5km individual time-trial from Beaujeu to Mont Brouilly, finishing with a tough 3km climb to the finish at an average 7.7 percent gradient.
Demare is not expecting to keep the yellow jersey.
"I've got better at time-trials but the final climb doesn't suit me," he said.
"In any case, I'll give it everything, you have to honour the yellow jersey."
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