The German speedster, leading a thinned-out group of sprinters at the finish, got his 14th victory in all competitions this year while Cavendish nursed wounds from a late crash as the race entered Normandy.
Swiss rider Fabian Cancellara got briefly held up by the trouble but didn't go down, and retained the overall lead for a fifth day after the 133-mile trek alongside the English Channel from Abbeville to Rouen.
The top standings didn't change: Bradley Wiggins, the leader of Cavendish's Team Sky hoping to be Britain's first Tour winner, is second, 7 seconds behind the Swiss leader. Defending champion Cadel Evans of Australia is 17 seconds off the pace in seventh.
With less than two miles left, a group spill brought down Cavendish, scraping up his rainbow-colored jersey of world champion. He looked a bit dazed as Sky staff checked him out and helped him get on a bike. He rode gingerly to finish the stage. The squad said he was banged up, but appeared to have no serious injuries and was likely to start today.
With Cavendish out of the picture, Greipel burst out of the depleted group of sprinters, and sped to the straightaway finish, a split-second ahead of Italy's Alessandro Petacchi and Dutch rider Tom Veelers.
The German said he didn't pay much attention to the late crash.
"I heard something behind me ... but at 60 kilometers per hour, you don't worry about what happened behind," the Lotto-Belisol rider told France-2 TV.
While pro cyclists all run the risk of crashing, Cavendish's spill amounted to a scare -- if faint -- to his high hopes of winning gold for Britain in the Olympic road race next month.
Cavendish has played second fiddle on Sky over the team's goal for Wiggins to get a victory, and unlike in years past has only one devoted lead-out man to guide and shield him in the frenzied last sprint: Bernard Eisel, an Austrian who also got banged up in the spill.
Cavendish, seen by many as the world's best sprinter and the winner of 21 Tour stages including Stage 2 Monday, conveyed no hard feelings over his mishap.
"Ouch.....," Cavendish wrote on Twitter. "Crash at 2.5km to finish today. Taken some scuffs to my left side, but I've bounced pretty well again. Congrats to (at)AndreGreipel."
Tyler Farrar, a sprint specialist from the United States who won the Tour stage on July 4 last year, also got tangled up and missed out on a chance for a repeat sprint victory on the U.S. Independence Day holiday.
In the pileup, the Garmin-Sharp rider flew off his bike, "somersaulted over his bars, tucked and rolled and ended up on his feet running away from the crash," tweeted team chiropractor Matt Rabin.
Despite the crash, Greipel said his victory was well-deserved.
"There were still really fast guys there for the sprint and I think we just deserve this victory," he said, playing down a question about whether he savored it less because Cavendish was knocked out.
"I think it's no question about that," Greipel added. "I won a stage in the Tour de France!"
At a still-young 27 years old, Cavendish, who was voted the BBC's sports personality of the year in Britain last year, has 21 stage wins at the Tour -- one short of the number that seven-time Tour winner Lance Armstrong had in his career.
An official race medical report said Cavendish sustained several scratches and a cut on a finger, Eisel sustained a gash that required stitches on his forehead, and Garmin's Robbie Hunter of South Africa scraped up his left side. Daniel Oss of Liquigas had a hip injury.
According to the Tour rulebook, riders who get delayed by a crash in the last three kilometers of the stage are awarded the same time as the stage winner.
The pack clocked the same time as Greipel -- 5 hours, 18 minutes, 32 seconds -- though some stragglers nursing wounds from crashes earlier this week, like world time-trial champion Tony Martin of Germany, and Tom Danielson of the United States, straggled in 2:21 behind.
Cancellara, who briefly got stalled by the crash, sighed with relief: "I'm really happy to get past that, a fall early hurts ... today it was calm, and then hectic at the finish."
David Moncoutie and Anthony Delaplace of France and Japan's Yukiya Arashiro broke away early and chiseled out a maximum lead of 8:40 at mile 10, but the pack reeled them in with about six miles left in the stage.
Riders set off from Abbeville -- a town where 6,000 buildings were destroyed or damaged in a German bombing raid in World War II in May 1940 -- and rode along the English Channel's picturesque, chalky cliffs with views of giant wind-turbine installations.
Today's fifth stage promises another bunch sprint, after a mostly flat 122-mile course from Rouen to Saint-Quentin north of Paris.
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