The Omega Pharma-Quickstep rider was part of an early break from the peloton, which managed to maintain its lead to the end of stage 13, allowing the British champion to edge ahead of Peter Sagan in a sprint finish.
"It was me on the podium but it should have been all of Omega Pharma-Quickstep. They were all just incredible. They rode from kilometre 60 and they rode their hearts out. They rode into the ground," Sky Sports News quotes the 28-year-old as saying.
"It was a difficult stage. It was a nervous stage but finally, I'm so excited to win, so happy to win. It's been a difficult few days and it's nice to be on the podium again. It wasn't really a master plan.
"We just felt the wind was in the right position so we started to ride a bit harder. We did it more to kind of make the peloton tired and finally it broke and we were racing."
Cavendish sits second in the points classification.