Featuring the Col du Pré and Cormet de Roselend climbs from the short 11th stage at this year's Tour, much was expected of the 110km stage from Frontenex to La Rosière and it delivered.
Bilbao hit the start of the tough final ascent with eight other breakaway survivors, countering strong attacks from Ian Boswell (Katusha) and Pierre Latour (Ag2R) to hit the lead seven kilometres from the top.
The Spaniard held a 21 second lead over the line ahead of runner-up Geraint Thomas.
“It’s really amazing," he said. "Yesterday, I had a bad day. I paid for my efforts from the Giro. I was completely done, I had no energy left, but today I felt good legs. I wanted to try something for the team who believed in me.
"It went perfect in the last climb. I had a small gap but I had to stay ahead before the last five kilometres. I knew it would be easier after that point. I managed to stay away. It’s unbelievable for me."
Thomas attacked Romain Bardet (Ag2R), Adam Yates (Mitchelton Scott) and Dan Martin (UAE) in the final kilometre but only after countering brief digs from Yates and Martin.
"It wasn’t ideal but AG2R rode really well today," Thomas said. "They really took the race on and put us under pressure. But fortunately we’ve got such a strong team, when one guys is not so good, another guy steps up.
"We were always just in control. We never panicked. But I didn’t want to get carried away. It’s easy to underestimate how far to go. I didn’t want to lose time. It’s obviously a big day as well tomorrow. I try to do just the minimum and at the end, I went for it to see what happens. I managed to get a few more bonus seconds, which is good.”
Another tale from the stage was the valiant effort of Movistar's Marc Soler. In the final 15 kilometres, the 2018 Paris-Nice champion bridged across to teammate Hector Carretero from the break attempting to take the race by the horns. But the pair did not survive Latour's attacks and languished in no man's land.
“We tried something in the finale," Soler said. "I felt good and I could take advantage of the help of my team-mate Hector Carretero. We didn’t win but we had to try.
"Tomorrow, it’ll certainly be a difficult and very fast day. I hope to finish the Dauphiné with the white jersey.”
Stage winner Bilbao was the last of a 27-rider breakaway formed in the early kilometres and featured the likes of Cataldo, Thomas De Gendt, and Warren Barguil.
Join us for the race finale as the peloton travails 136 kilometres and five categorised climbs to Saint-Gervais Mont-Blanc. Watch it LIVE streamed here and broadcast on SBS Viceland from 9.35pm AEST.