The Frenchman won the 158.5km stage, which started in Annecy, in a time of 4:25:27. He was followed home by Bahrain-Merida’s Jon Izaguirre Insausti and Direct Energie’s Rein Taaramäe.
BMC Racing Team’s Greg van Avermaet extended his overall lead.
Today’s stage, which came after the first rest day, featured four major climbs and was the first of three days in the Alps.
There was also an early intermediate sprint before the first major climb, which was won by Bora-Hansgrohe’s Peter Sagan.
Before the stage began Movistar’s Mikel Landa was involved in a crash with Quick-Step Floors’ Fernando Gaviria in the neutral zone. Landa was still taking care of his battle wounds from his crash during Sunday’s cobbled stage.
With less than 80km remaining today, defending champion Chris Froome suffered a puncture on a gravel section. His Sky teammate Jonathan Castroviejo assisted him with a wheel change, which allowed Froome to resume his chase.
About 60km from the end, a large break of 18 riders had a gap of seven minutes and 40 seconds to the peloton. This group included the yellow-jersey wearer.
The gap narrowed to six minutes and 20 seconds with 39km to the finish.
The leading group included stand-out climbers such as LottoNL-Jumbo’s Robert Gesink, Dimension Data’s Serge Pauwels, Groupama-FDJ’s David Gaudu, Wanty-Groupe Gobert’s Guillaume Martin, Izaguirre and Alaphilippe.
Quick-Step Floors’ Philippe Gilbert was immediately dropped from the peloton when riders reached the Col de Romme, which featured an elevation of 1 297m. This was soon followed by an attack from Fortuneo-Samsic’s Warren Barguil.
Barguil was out on his own with a decent gap to the peloton as he chased the break, but it was short-lived as he made contact with them again.
With less than 30km remaining Taaramäe was right at the front with a half-minute lead over the seven chasers.
In the final 2km of the climb, which was 8.8km long with an average gradient of 8.9%, he was eventually caught by Alaphilippe.
Alaphilippe rode away from Taaramäe and claimed maximum points at the summit of Col de Romme, with the latter joining him on the descent as they made their way to the Col de la Colombière mountain pass.
Alaphilippe, who missed the race last year due to injury, proved too fast for him and rode solo with a five minutes and 40 seconds gap to the peloton when they had 25km to go to the finish.
Taaramäe was 15 seconds behind the leader and the rest of the chasers were over a minute back when Alaphilippe started tackling the 7.5km Colombière.
With 18km remaining Alaphilippe, who won this year’s La Flèche Wallonne, was one minute and 18 seconds ahead of his closest rival Taaramäe, who was later caught by Izaguirre.
The latter was second over the top, one minute and 30 seconds behind the leader, and was followed by Taaramäe, Van Avermaet and Pauwels.
Alaphilippe extended his lead as he reached the narrow descent and false flat in the final 2km to Le Grand Bornand.
“There’s a lot of emotion, because winning at the Tour is not easy. I came close in my first Tour two years ago, and to win in this way, it’s unexpected because . . . I don’t even have the words,” said the stage winner.