The 160 remaining riders had to contend with rain soon after the start in Nantua and intermittently along the route.
Groves was then part of a 13-man breakaway that was formed after the second of the day’s four categorised climbs.
His compatriot Harry Sweeny attacked over the day’s penultimate climb and went clear of Jordan Jegat with 54km to go, but the EF Education-EasyPost rider was caught on the first slopes of the final ascent.
Local favourite Romain Gregoire and Spanish debutant Ivan Romeo attacked on the downhill but as they sped into a wet turn, both slipped to the tarmac, with 21-year-old Romeo coming off worse as he also slid into the kerb.
Groves was right behind them so watched it all unfold and sensed his opportunity, attacking with 16km remaining.
Frank van den Broek and British rider Jake Stewart merely looked at each other, with that momentary stalemate allowing Groves to go clear.
He gradually increased his lead to the line, where he was sobbing after clinching an emotional victory.
“The team gave me a free role in the last few days,” Groves added. “We weren’t sure if I should go for it today or wait until tomorrow. But when the rain falls, I always have a super feeling normally, in the cold weather. It’s my first time winning solo – and it’s in a Tour stage, [so] pretty incredible.
“There’s so much pressure at the Tour. Having won in the Vuelta and the Giro, I always get asked whether I’m good enough to win in the Tour – and now I’ve shown them.
“I tried to play my cards right and get into an early move. But the uphill start made that incredibly difficult. When I made the decision, I knew that [Matteo] Jorgenson and [Tim] Wellens would watch each other, so I tried to distance myself form them.
“Then after the crash, Van den Broek goes full, so I closed that. Then him and Jake Stewart watched each other and I had a gap with 16km to go, so I rode full until the final 200m.”
Jonas Vingegaard looked resigned to defeat, having been unable to significantly cut Pogacar’s lead on two gruelling days in the Alps.
When the two-time Tour winner did not contest the first categorised climb, it meant Pogacar secured his third King of the Mountains title on the Tour.
While Pogacar will not be attacked on the final day in Paris, a prestigious stage win will be up for grabs on the Champs-Elysees.
