The 26-year-old proved the strongest of a huge breakaway, pulling away from Alejandro Valverde (Movistar) on the ascent of the Col de Beixalis before descending smartly to seal Jumbo-Visma’s second stage win of the race following Wout van Aert’s win in Stage 11.
“It’s incredible, I’m lost for words," Kuss said after the finish. "To be honest, I was really suffering a lot in this Tour, I didn't feel like I had the spice in the legs.
"Today I knew the finish was near where I live so I was really motivated for the stage and finally I had really good legs again, so I'm so happy."
Tadej Pogačar (UAE Team Emirates) finished with the group of GC contenders to maintain his overall lead, while Wout Poels (Bahrain Victorious) overtook Michael Woods to don the King of the Mountains jersey and Mark Cavendish (Deceuninck-QuickStep) avoided the time cut to retain the green jersey.
The Tour de France headed into Andorra for Stage 15, the mountainous journey over the Pyrenees set to head over the highest point for this year's race, the Port d’Envalira, 2,408 metres above sea level.
The break established itself relatively early in the race, a group of 32 riders escaping with relatively little resistance from the peloton. The group comprised Wout van Aert, Steven Kruijswijk, Sepp Kuss (all Jumbo-Visma),Dylan Teuns, Wout Poels, Matej Mohoric (all Bahrain Victorious), Vincenzo Nibali, Kenny Elissonde, Julien Bernard (all Trek-Segafredo), David Gaudu, Valentin Madouas, Bruno Armirail (all Groupama-FDJ), Dylan van Baarle, Jonathan Castroviejo (both INEOS Grenadiers), Julian Alaphilippe, Davide Ballerini (both Deceuninck-QuickStep), Michael Woods, Dan Martin (both Israel Start-Up Nation), Neilson Powless, Ruben Guerreiro (both EF-Nippo), Alejandro Valverde (Movistar), Nairo Quintana (Arkéa-Samsic), Michael Matthews (Team BikeExchange), Pierre Latour (TotalEnergies), Thomas De Gendt (Lotto Soudal), Lukas Postlberger (Bora-Hansgrohe), Ion Izaguirre (Astana-PremierTech), Aurélian Paret-Peintre (AG2R Citroën), Sergio Henao (Qhubeka-NextHash), Mark Donovan (Team DSM), Ruben Fernández (Cofidis) and Franck Bonnamour (B&B Hotels).
The peloton were happy to let the group go free and build up a big lead, with Paret-Peintre the highest-placed rider in the group, in 13th and over 24 minutes behind Tadej Pogačar's race lead.
Matthews followed an attack that went off from the big group, and claimed the intermediate sprint in a close-run affair with de Gendt and Ballerini. He moved 20 points closer to Mark Cavendish's lead in the classification, which sits at 72 points. That group was brought back into the fold of the larger break.
The gap continued to grow until well into the stage, with Groupama-FDJ driving the pace within the escapees with Amirail pulling a very long turn. The first king of the mountains point, the Montée de Mont-Louis, saw hot competition with Wout Poels launching a fierce sprint up the shallower gradients with van Aert and Woods trying to match him to stay up in the standings for the mountains classification.
Poels took out the sprint to the top to claim 10 points, with van Aert taking 8, Woods 6, and previous mountains jersey-holder Quintana curiously not getting involved in the battle.
De Gendt tried to use the momentum through the mountain sprint to launch his own attack, but he was marked by the riders who had sprinted for the points and was soon brought back into the main move.
The breakaway stayed under the power of Amirail all the way into the Col de Puymorens, with the gap to the breakaway out to just under 10 minutes as the riders commenced the category 2 ascent.
That gap went to over 10 minutes at the foot of the climb as Amirail tirelessly continued to set the pace, with no signs yet of a move from the GC contenders in the UAE-led peloton.
Poels and van Aert exploded off the front of the break 300 metres from the KOM point with Woods in hot pursuit as Quintana tried but failed to follow. The Belgian had the better legs in the battle, taking the maximum 5 points with Poels settling for 3, Woods 2 and Valverde 1.
There was movement in the peloton as they made their way up the category 2 ascent as the Movistar train came to the fore led by Ivan Garcia Cortina with Richie Porte (INEOS Grenadiers) fighting for position on his wheel with his team close behind.
Riders began to fall off the back as the pack crested the climb, the pace too much with Chris Froome (Israel Start-Up Nation) and Sonny Colbrelli (Bahrain Victorious) both dropped before the summit.
Nibali's Trek-Segafredo teammates finally took over from Groupama-FDJ at the head of the break, as the climb to the highest point on this year's Tour, the Port d’Envalira began.
Woods went early for the points 2.8 kilometres from the peak of the climb but was marked by Kuss as Nibali and Powless followed.
Quintana attacked clean off the front 1.4 kilometres from the summit, taking advantage of a strong tailwind as his pursuers failed to bridge across, the Colombian taking the maximum 10 points as van Aert outsprinted Poels again with Woods and Valverde behind.
Geraint Thomas (INEOS Grenadiers) led the peloton to the summit with teammate Richard Carapaz tucked in behind as they pulled back more time on the break, the gap down to five minutes and 18 seconds as they crested the Port d’Envalira.
Splits formed with speeds picking up to as much as 84 kilometres on the descent, second-placed GC contender Guillaume Martin (Cofidis) distanced from the yellow jersey group as he was forced to pedal hard onto the wheel of Mattia Cattaneo (Deceuninck-QuickStep) in an attempt to re-join.
The pair were ultimately unsuccessful as the gap widened, Martin’s huge effort in stage 14 to move up perhaps contributing to his downfall as he saw his GC hopes take a big hit on the long descent.
INEOS continued to do the work in the favourites group as van Aert took the lead in the reduced breakaway five minutes ahead with 25 kilometres left as the final climb of the category 1 Col de Beixalis approached.
Quintana went again on the attack on the start of the climb but was reeled in and then was dropped shortly after, Kuss surging to the front and then dropping Valverde with five kilometres to the summit.
Kuss quickly pushed out his lead to 30 seconds over Valverde and was able to maintain that advantage to the top of the climb as the race for yellow opened up behind.
Carapaz led the attacking followed closely with Pogačar, Jonas Vingegaard (Jumbo-Visma), Rigoberto Uran (EF Education-Nippo) and Australian Ben O’Connor (AG2R-Citroen) prominent among the group of ten contenders.
O’Connor launched his own attack but was caught almost instantly before Pogačar and Vingegaard began a battle for control at the front inside a kilometre from the summit.
Uran, Carapaz, Vingegaard and O’Connor all tried attacks in the final section of the ascent but the GC group remained tight on each other’s wheels, with O'Connor paying the price for his aggression as he was dropped just before the summit.
A scorching descent from Kuss into Andorra-la-Vielle enabled him to maintain his lead on Valverde soloing home for the stage victory with Valverde with Poels winning the sprint from a group of five for third.
Van Aert had dropped back to the yellow jersey group and took to the front the set the pace and further distance the dropped duo of Martin and Alexey Lutsenko (Astana-Premier Tech) the front of the now seven-strong yellow jersey group as they reached the bottom of the climb with O’Connor managing to re-join Pogačar, Uran, Vingegaard, Carapaz, and Kelderman, finishing together as Uran moved back into second overall.
The Tour de France has a rest day tomorrow, but will recommence with a medium mountains stage from Pas de le Case to Saint Gaudens. Watch the race on Tuesday from 2030 AEST on SBS and SBS OnDemand with the race action starting on the SKODA Tour Tracker at 2055 AEST.