Kittel, who won the first and 10th stages, stayed behind the Briton's wheel in the final straight and went past Cavendish at the very last moment.
Britain's Chris Froome avoided a late pile-up in the bunch and retained the overall leader's yellow jersey.
Kittel became the first German rider to win three stages in the same Tour since fellow sprinter Erik Zabel in 2001.
With Tony Martin winning Wednesday's time trial and Andre Greipel taking the sixth stage in a sprint, German riders have now won five stages on the Tour.
"I can go back and look at it over again, he was just faster," Cavendish told reporters.
"I don't think myself or the team could have done anything different. He was just simply better, you know? The guys were really really incredible for me today.
"It was a good duel between Omega Pharma-Quick Step and Argos and ultimately the guys went at the right time. They delivered me at the right time. I was just beaten by a better guy," added the Manxman.
Slovakia's Peter Sagan took third place at the end of the 218-km flat dash from Fougeres. He leads the points classification with 307 and Cavendish moved up to second on 211.
The top positions in the overall standings remained unchanged with Froome leading Spain's Alejandro Valverde by 3:25 and Dutchman Bauke Mollema by 3:37. Fourth-placed Alberto Contador of Spain is 3:54 off the pace.
Dozens of riders were involved in the crash but as it occurred inside the last three kilometres all were credited with the winner's time.
SHOULDER FRACTURE
Froome's team mate Edvald Boasson Hagen was one of those affected and the Norwegian was later forced to pull out of the race with a shoulder fracture.
"Edvald Boasson Hagen has been forced to abandon the Tour de France following a fractured right scapula on stage 12," Team Sky said in a statement.
"Fortunately this doesn't require surgery but Edvald will return home to Norway for further investigation and treatment."
It is the second time in this year's race Kittel has beaten Cavendish in a sprint.
Another specialist, German Andre Greipel, did not contest the finale having been held up behind the crash.
Five men formed an early breakaway to open a nine-minute gap but the sprinters' teams reeled them in with five kilometres left.
Both Kittel's Argos-Shimano and Cavendish's Omega Pharma-Quick Step teams took the front to lead their sprinters. Kittel, with no lead-out man left, took Cavendish's wheel and perfectly timed his final effort.
"It's crazy, I'm speechless. My team really worked well today," he said.
"As we say in Germany, good things come by three. I want to congratulate (team mate) Tom Veelers for his hard work despite what happened to him," Kittel added.
On Tuesday, Dutchman Veelers crashed in the finale after bumping shoulders with Cavendish, who was cleared of wrongdoing by the race commissaires.
Friday's 13th stage takes the peloton over 173 km from Tours to Saint Amand Montrond.
