Kristoff, the reigning Milan-San Remo champion, sprung off the wheel of his Katusha lead-out man Luca Paolini to surge to a comfortable win ahead of Cannondale's Sagan and the French national champion Arnaud Demare (FDJ).
A crash with 3.5km remaining of the 185.5km stage from Bourg-en-Bresse meant Andre Greipel, the German national champion from Lotto Belisol, could not contest the bunch sprint. Griepel's compatriot Marcel Kittel - the triple stage winner from Giant-Shimano - was also absent after being distanced on the last of four lower category climbs on a sweltering day in the Rhone.
Vincenzo Nibali (Astana) finished safely to retain his leader's yellow jersey ahead of Friday's visit to the Alps, a high altitude summit finish at Chamrousse.
"It's a great feeling," said 27-year-old Kristoff after the first Tour stage win of his career. "I've been dreaming about this moment since a child. I've had a couple of second places this year - and last year - so it's great to go one better."
Kristoff's strong kick also saw off the challenge of Switzerland's Michael Albasini (Orica-GreenEdge) and Lituania's Ramunas Navardauskas (Garmin-Sharp) who completed the top five.
"I was so happy when I looked round and saw that no one would pass me. Tonight there will be a big celebration with champagne - but not too much because it is a very hard day tomorrow," Kristoff added.
FIVE-MAN BREAK: Sebastien Langeveld (Garmin-Sharp), Simon Clarke (Orica-GreenEdge), Florian Vachon (Bretagne-Seche), David de la Cruz (NetApp-Endura) and Gregory Rast (Trek Factory Racing) formed the day's decisive break after an early attack as temperatures rose to the high 30s.
The break established a maximum lead of five minutes as they passed the vineyards and chateaux of the Rhone. Then, with 90km remaining, disaster struck when De la Cruz's front tyre slipped in the soft tarmac sending the Spanish debutant tumbling to the ground on a tight bend. Langeveld, the Dutch national champion, also came down in the incident - but it was De la Cruz who came off the worst: forced out of the race with a suspected broken collarbone.
Both Rast and Vachon soon wilted in the heat as Europcar and Giant-Shimano led the chase back in the peloton. Europcar's plan became all the clearer when Perrig Quemeneur and Cyril Gautier attacked on the final climb of the day, the Cat.4 Col de Grammond, 30km from the finish. Clarke put in his own attack to distance his former team-mate Langeveld, and the trio rode over the summit with just one minute to play with on the rampaging peloton.
Quemeneur threw in the towel with 10km remaining before Gautier and Clarke jostled around until being swallowed up inside the final 5km. As the teams of the main sprinters competed for positions, Andre Greipel (Lotto Belisol) touched wheels with Sylvain Chavanel (IAM) and the pair hit the deck.
Greipel and Chavanel were still arguing about who was responsible for the incident as the peloton swept under the flamme rouge and the final sprint opened up. Despite some hefty work by Giant-Shimano, Germany's John Degenkolb was nowhere to be seen - and despite momentary resistance from Sagan and Demare, Kristoff was on hand to take a routine stage win on the eve of the Alps.
RIDE OF THE DAY: Simon Clarke's class and strength came through after a solid stint in the break but Kristoff deserves special mention for his persistence. The Norwegian opened up his Tour de France account and rewarded his Katusha team for their efforts in the closing kilometres. A strong win for a classy competitor.
DAY TO FORGET: Germany may have notched five of the first nine stages - plus added the World Cup during the process - but things did not exactly go according to plan in stage 12. Triple stage winner Marcel Kittel was expected to be shelled out on the climbs, but his understudy John Degenkolb was nowhere to be seen in the final sprint, while Andre Greipel's chances took a tumble along with his trademark huge thighs with 3.5km remaining. A stage top ten without a German flag on it has been a rarity in this year's Tour.
COMING UP: Friday's 197.5km stage enters the Alps with the race's first HC climb: the summit finish at Chamrousse, which rises for over 25km and is a real leg-sapper - especially in the expected heat. Before that, the small matter of the Cat.1 Col de Palaquit with its irregular, double-digit ramps.
PLAT DU JOUR: Seeing that we're heading near Savoie then it would be a shame not to load up the calorie deficit with a good fondue savoyarde - perhaps with a side salad pebbledashed with local Grenoble walnuts. Follow this up with some chartreuse - legendary green digestif made by monks - and you're onto a winner.
- Sports & Recreation
- Andre Greipel
- Marcel Kittel
- Simon Clarke
- Lotto Belisol
- Arnaud Demare