Jungels went clear with 65 kilometres to go on the day and never looked back, steadily gaining ground on the breakaway and holding off a late attack from Thibaut Pinot (Groupama FDJ) who began desperately chasing in the final 20 kilometres.
The 29-year-old crossed with daylight between him and the next rider, twenty-two seconds ahead of Jonathan Castroviejo (INEOS Grenadiers) in second and Carlos Verona (Movistar) a further four seconds back, the Spanish duo catching an exhausted Pinot in the final 300 metres.
The win was a huge moment for the Luxembourgian, who has battled arterial endofibrosis, a condition that reduces blood flow to the legs which tends to impact cyclists in particular, over the last two years.
"It's hard to say how I feel right now, I'm just overwhelmed," Jungels said following the stage.
"This is huge, this is what I came here for after a couple of years of struggling, a very tough year last year with surgeries and everything.
"To take the victory this way, it's my style of racing and I'm super happy."
The day's break got away after 50 kilometres of racing, a big group with Jungels, Wout van Aert (Jumbo-Visma), Patrick Konrad (BORA-Hansgrohe), Warren Barguil (Arkea-Samsic), Rigoberto Uran (EF Education EasyPro), Jonathan Castroviejo (INEOS Grenadiers), Thibaut Pinot (Groupama FDJ), Franck Bonnamour (B&B Hotels), Carlos Verona (Movistar), Simon Geschke (Cofidis), Luis Leon Sanchez (Bahrain Victorious), Kobe Goossens (Intermarché–Wanty–Gobert Matériaux) , Joe Dombrowski (Astana), Jasper Stuyven (Trek-Segafredo), Guy Niv and Hugo Houle (both Israel Premier-Tech).
The group mostly stayed together until the Col de la Croix, when Jungels made his move off the front with 65 kilometres left and began to stretch out a gap on the descent, pedalling hard to gain as much ground as possible through the towns near the Swiss-French border.
His lead was at a minute and a half when he hit the Pas de Morgins with 32 kilometres to go, and went out to over two minutes as the climbing started, until Pinot took off in hot pursuit with under 20 kilometres to go to bring the gap back down.
Pinot got as close to 20 seconds to Jungels on the lead-in to the finish, but began to falter in the last kilometres and the 2018 Liege-Bastogne-Liege winner added a special victory at the Tour de France to his resume.
"I had to go from far out today, because it would have been impossible to ride away from the favourites in the last climb," Jungels said of the strategy behind the move.
"I thought I could make up some time on the downhill, I knew I wouldn’t explode, but the last two kilometres were endless. I took all the risks I could and it happened.
"I just want to thank my team and everyone who kept faith in me in the last few years. I’m just grateful.”
The Tour de France now enters a rest day, with racing resuming on Tuesday night (AEST) with a 148-kilometre stage from Morzine les Portes du Soleil to Megeve. Watch all the action live from 9:20pm AEST on the SBS SKODA Tour Tracker, or 9:30pm AEST on SBS and SBS On Demand.
