France have now won two consecutive Monuments for the first time since 1992 after Thibaut Pinot won last year's Lombardia.
Last year's winner Vincenzo Nibali, three-times world champion Peter Sagan and reigning world champion Alejandro Valverde were also in the small lead group that broke clear off the Poggio, but when a game of cat and mouse developed on Via Roma it was Alaphilippe who made the decisive move.
Slovenia's Matej Mohoric (Bahrain-Merida) took it on initially but Alaphilippe was quickly locked onto his back wheel and surged past, punching the air as he crossed the line.
The red hot 26-year-old Deceuninck-Quick Step rider now has seven victories this season, having also won the Strade Bianche.
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Belgium's Oliver Naesen (AG2R La Mondiale) was second with Team Sky's Polish rider Michal Kwiatkowski third.
To beat such a powerful group in such high-pressure circumstances was proof of just what form Alaphilippe is in.
"It's difficult to realise what I did and what my team did. They protected me all day," an emotional Alaphilippe said.
"I was really focused to control the attack and with 600m to go when Mohoric went to attack I said 'It's now or never'.
"I made a big effort at the top of the Poggio. At the end I was only with strong riders and I tried to recover in the downhill. In the last two kilometres I said I want to win -- no second place."
(Reporting by Martyn Herman; Editing by Ian Chadband and Toby Davis)
