RODEZ, France >> Greg van Avermaet of the BMC team won Stage 13 of the Tour de France with a finishing burst of speed Friday that pushed Peter Sagan into second place for the fourth time at this year’s race.

Sagan was kicking himself after he eased up in the final meters (yards).

"My stupid mistake," said the Tinkoff-Saxo rider.

For most of the flat-to-hilly stage from Muret deep in southern France, a group of six low-placed riders rode in a breakaway at the front of the race. But the trailing main pack of riders sped up furiously as the finish in Rodez approached and caught the last of the escapees inside the last kilometer (last half-mile).

In the final uphill sprint, Van Avermaet and Sagan surged to the front. The Belgian rider won that duel by just a few meters. Feeling that a rider — he didn’t know it was Sagan — was still on his wheel, the stage winner pushed to the very end. Sagan was up in his saddle, sprinting behind him, but mistimed his finish, sitting back down too early.

"I’m very angry and disappointed," Sagan said. "I sat down and all the pain comes. Bad."

Race leader Chris Froome and his closest podium challengers finished safely, all throwing themselves into the final sprint up the last hill because they didn’t want to lose time, even just a few seconds, to each other. Froome’s lead remains unchanged, with Tejay van Garderen of BMC still 2 minutes, 52 seconds back and Nairo Quintana still third, 3:09 back.

"It turned crazy at the end," Froome said of the finish. The British leader of the Sky team was happy that he has one less stage to complete before Paris, but is bracing for another battle with podium contenders on the short but very sharp uphill finish of Saturday’s Stage 14 at Mende.

Van Avermaet said winning was "incredible."

"I was dead, really dead," he said. "I thought I’d caught second. I pushed for the line and was so happy he didn’t overtake me."

The breakaway group of riders, none of them a threat to Froome’s lead, rode off from the start of the 123-mile trek that took the Tour past plantations of yellow sunflowers and golden fields of harvested wheat.

The peloton let the escapees get away, hoping for a breather after three grueling days of climbing in the Pyrenees and under unrelenting sun that melted tarmac. Riders gulped liters (pints) of liquid and doused themselves as temperatures soared into the mid-30s Celsius (mid-90s Fahrenheit).

But even easier stages like this one hide hazards: Last year’s runner-up Jean-Christophe Peraud, leader of the AG2R La Mondiale team, suffered a nasty spill at speed on the flat, tearing strips of skin off his left leg and arms as he hit the deck hard and rolled several times. The French rider gingerly picked himself up and got back on his bike, gritting his teeth. A Tour doctor then patched him up on the move, wrapping his wounds in bandages as Peraud gripped onto the speeding medical car.

Peraud said: "Stupidly, I was looking backward," searching for a teammate, and that he didn’t see a rider who veered in front of him.

Like mice hoping to escape a hunting cat, the escapees rode hell for leather into Rodez, a town of 26,000 people in the rural Aveyron region. Its speciality dishes include aligot, a mix of melted cheese and mashed potato, and tripe.

But the cat won. The speeding peloton swallowed up the last of them in the final sprint, and they were too tired to prevent Van Avermaet from claiming the win.