The Orica-Scott rider jumped away from a group of leading riders near the top of the Col de Bourigaille, 19.5 km from the finish line up the Mur de Fayence, a punishing 1.3 km climb at an average gradient of 9.8 percent.
"I was quite far out in the general classification (GC) this morning so I had a bit of freedom," Yates said.
"I hoped I would be joined by other riders but I was on my own so I just had to go full gas until the end."
Yates is now eighth overall, 1:37 behind Alaphilippe.
"If I wanted to win the GC I had to try and take time back somewhere. But there is still quite a lot of time to regain. Alaphilippe is a phenomenal rider, one of the most gifted of our generation," Yates said.
Sergio Henao (Sky) attacked with 1km left to take second place and finish second to move up to third overall, 46 seconds off the pace.
Henao is expected to further threaten Alaphilippe's lead in Saturday's decisive so-called "queen stage", a 177-km trek featuring three category one ascents.
Alaphilippe (Quick-Step Floors) ended up fourth on the day, 29 seconds behind Yates and 12 adrift of Henao, who also bagged six seconds in time bonuses.
Among the favourites, Alberto Contador (Trek-Segafredo) and Ilnur Zakarin (Katusha) finished 32 seconds off the pace.
Two-time winner Richie Porte (BMC) finished 26 seconds adrift of Yates and 17 behind Henao and now sits 15th on the general classification with two stages to go.
The 177km seventh and penultimate stage concludes with a 15.7km climb up to the 1678m col de la Couillole, the highest finish in the race's 75-year history.
"A rider like Henao can build up gaps on a long climb like that, but he's not the only one, I have out watch out for others too," Alpaphilippe said.