Alaphilippe rode clear with the Astana rider with around 15km to go in the approach to Siena.
Wout van Aert (Jumbo-Visma) caught the pair with 1.2km to go but was distanced in the final battle and finished 27 seconds adrift.
“It’s unbelievable,” said Alaphilippe. “I was focused all day on the finale. I was lucky to never crash nor have a flat tyre. My team did a great job in protecting me.
"Jakob Fuglsang was very strong, but I made no mistake. However, I wasn’t confident in winning until the last corner. This is a wonderful victory.”
The finish: See how Alaphilippe claimed Strade Bianche crown
It was the first victory for a French rider at the Spring Classic, and QuickStep’s third WorldTour one-day victory of the season following Elia Viviani's win in the Great Ocean Road Race and Zdenek Stybar's triumph at Omloop Het Nieuwsblad last weekend. Stybar came fourth in Strade Bianche.
Kuurne-Brussels-Kuurne was also won by Bob Jungels, while Florian Senechal topped the podium at Le Samyn.
Earlier, Team Sky’s Diego Rosa opened up a gap of 1:30 with his breakaway at the 50km mark across the white gravel of Tuscany.