France's Thomas Voeckler kept the yellow jersey after nestling safely in the main pack for most of the 98-mile route from Aurillac to Carmaux.
Wednesday's 11th stage is another flat route for sprinters before riders reach the gruelling climbs of the Pyrenees.
Defending champion Alberto Contador and his main rivals - Luxembourg's Andy Schleck and Australia's Cadel Evans - all finished without losing any time to one another. Contador was riding with a sore right knee.
"I'm feeling better and better," he said. "At the beginning of the stage, I wasn't sure what to think, but as the stage progressed my knee was feeling less sore."
Schleck, runner-up to Contador in the last two Tours, remains 1:30 ahead of the Spaniard in the overall standings, and 11 seconds behind Evans, a two-time Tour runner-up.
Voeckler, who also wore the yellow jersey in 2004, was near the front of the pack as the sprint began and was happy to get to the line without incident. The first nine stages of the race were marred by crashes and injuries.
"The yellow jersey comes with a lot of tension, a lot of stress," Voeckler said. "But in terms of the fans it's a fabulous thing."
Cavendish seemed to have sealed his third stage victory of this year's Tour when he turned into the final straightaway. But Greipel stormed past him in the last 20m with a late burst and punched the air in delight as he crossed the line.
"I didn't commit early enough, I didn't kick," Cavendish said. "I kind of rolled round the last corner. ... Greipel just came past me and beat me."
Greipel, who rides for the Omega Pharma-Lotto team, looked tearful on the podium as he celebrated.
"It's the moment I've been waiting for all year," he said. "It's the most beautiful race in the world and the most famous. To win here is sensational."
Jose Joaquin Rojas of Spain was third. The main pack all finished in 3hr 31min 21sec.
Greipel was beaten to the line by Cavendish in the seventh stage last Friday in Chateauroux after being the one to attack too soon. This time, Cavendish gave credit where it was due.
"Now I'm happy for him. He's come to the Tour de France and he's won," Cavendish said. "I feel I made a mistake, but Greipel beat me so there's not an excuse I can say."
Cavendish and Greipel feuded last year when they were both on the HTC-Highroad team. The tense relations are improving.
"We had a chat after the Chateauroux stage and he said 'I have a big respect for your sprint'," Greipel said. "He was not always really friendly with his comments (about) me."
An early breakaway of six riders was cut down to three when Frenchmen Arthur Vichot and Sebastien Minard were joined by Italian Marco Marcato at the base of the 2.5-mile ride up Cote de Villefranche-de-Rouergue.
The pack caught Vichot and Minard with about 11 miles remaining, leaving only Marcato in front. But Marcato's lead didn't last much longer. A new group of five, featuring the yellow jersey of Voeckler and green shirt of Philippe Gilbert, surged ahead in the last six miles.
Gilbert, the winner of the opening stage, then accelerated ahead in a bid for a spectacular victory. But the Belgian had far too much road left, and the pack soon swallowed him up.
Norway's Thor Hushovd, who lost the yellow jersey to Voeckler on Sunday, was briefly delayed near the end when he had to pull over to put his left shoe back on.
