Led by his teammate Remco Evenepoel in the last kilometers, Alaphilippe failed to repeat his performance the day before in Viana, ahead of the line by Bilbao, from Guernica, nearby.
Russian Aleksandr Vlasov finished third in the stage, just ahead of another Frenchman, David Gaudu.
The third Frenchman in the top 10 of the stage is Pierre Latour, 6th.
Overall, Primoz Roglic keeps the lead, but the top 10 is slightly modified: Rémi Cavagna, Geraint Thomas, Bruno Armirail and Ben Tulett are left behind, and Vlasov is getting closer to third place, Bilbao passes 5th, and Alaphilippe climbs to tenth place, 28 seconds behind the Slovenian leader.
Three riders formed the breakaway of the day: Slovenian Jan Polanc, Canadian Hugo Houle and Spaniard Cristian Rodriguez, who resisted alone up to 17 kilometers from the line.
Bilbao has tried several times to escape, believing not to make the weight in the sprint against the world champion, but it is finally with regularity that he imposed himself on the line.
"It's hard to describe what it's like to win at home after so many attempts... Finally! And in addition to the sprint, in front of a world champion", reacted Bilbao on arrival.
For his part Alaphilippe regretted having launched his sprint "a little too early".
"In the final, Remco did an exceptional job for me again. Unfortunately, my legs still hurt really badly. And I came across a very strong Pello Bilbao".
Frenchman Julian Alaphilippe, after the arrival of the 5th stage of Tirreno-Adriatico, March 11, 2022 in Fermo Luca Bettini AFP / Archives
On Thursday, the fourth stage (185.6 km) will take the riders from Araba's capital, Vitoria-Gasteiz, to Zamudio, very close to Bilbao.
Four difficulties will punctuate the day, two first 3rd category bumps, and two others of 2nd category: the steep climb to Urruztimendi (1.9 km at 10.5%), and the second climb to Vivero (6 km at 6 2%), which promises to be decisive, twenty kilometers from the line.
© 2022 AFP