Quick-Step Floors' Alaphilippe outsprinted Daniel Martin of UAE Team Emirates to win the 181-kilometre fourth stage from Chazey-sur-Ain to Lans-en-Vercors.
Astana's Dario Cataldo, who was leading for most of the race, finished in 12th place after he was overtaken by the chasing pack with just 300 meters to go.
Team Sky now hold the top three spots in the general classification, with Moscon ahead of team mates Kwiatkowski and Geraint Thomas both by six seconds.
The 130-kilometre fifth stage on Friday will see riders head into the mountains between Grenoble and Valmorel.
The Dauphine is the main warm-up race for the July 7-29 Tour de France.
(Reporting by Arjun Panchadar in Bengaluru; Editing by Hugh Lawson)