The 27-year-old claimed his 10th victory of the season, having also won the one-day Milan-San Remo, Fleche Wallonne and Strade Bianche.
He also claimed two stage victories and the best climber's polka dot jersey on the 2018 Tour de France.
"I don't know yet if I'll start the Tour in top condition or race for the polka dot jersey. We'll see after the Dauphine," said Alaphilippe.
Britain's Adam Yates retained the overall leader's yellow jersey ahead of Saturday's 'queen' stage of a race which has been overshadowed by four-time Tour de France champion Chris Froome's horrific crash on Wednesday.
Alaphilippe and Austrian Muehlberger escaped from the peloton only 12 kilometres into the 228km ride from Saint-Vulbas to Saint-Michel-de-Maurienne, alongside Alessandro de Marchi.
Italian De Marchi was dropped on the eighth and final climb of the day, about 10km from the finish, leaving Alaphilippe and Muehlberger to fight it out for the win, with the home favourite taking the spoils.
"It was a soft sprint after such a long and difficult race," added Alaphilippe.
"On the last climb, I tried two or three times to accelerate but I couldn't tell the difference."
The main group of overall contenders, including Yates, crossed the line six minutes and 10 seconds adrift.
Mitchelton-Scott rider Yates remains four seconds clear of Belgian Dylan Teuns in the overall standings, with American Tejay Van Garderen just two seconds further behind.
Saturday's seventh and penultimate stage ends with the punishing climb at Pipay, which lasts for 19km with an average gradient of 6.9 percent.
The majority of riders are using the eight-day race as their final warm-up for the Tour de France which starts on July 6 in Brussels.