The Spaniard evaded a felled Valerio Conti (UAE) on the final right-hand bend to launch his winning bid from Giovanni Visconti (Bahrain-Merida) and Luis Leon Sanchez (Astana). Led by Enrico Battaglin (LottoNL-Jumbo), the peloton trailed closely behind at just 12 seconds.
The quartet with Gregor Muhlander (Bora-Hansgrohe) formed a decisive split from another group of around 16 escapees on the uncatgeorised Coppa del Fornaro climb, with just six kilometres left to race.
The original breakaway group was kept to just an average of two minutes by a speedy peloton, driven by Quickstep and Katusha. On the descent of the category two Sant'Angelo, 80 kilometres from the finish, Izagirre found himself in the leading group.
"It wasn't our plan to enter the break," Izagirre said "But we saw a chance into that long descent, we also had to keep riders from dangerous teams at reach, and so we decided to give it a try and carry on later on once we made it.
"I'm so glad we could finish it off. When Conti crashed just in front of me I was a bit hesitant, because there was still around one kilometre remaining. However, I looked back, saw that there was a split in our group, and I chose to go on full steam until the very end."
It's Izagirre's first grand tour stage win and adds to the family's Giro collection after his brother Ion's victory on stage 16 in 2012.
"I'm just incredibly happy that I got this. This victory means a lot to me, it's the biggest I've ever achieved."
"I've spent so many years chasing a Grand Tour stage success, so many times into breakaways, many close calls, and reaching it in such a Giro stage - this is amazing.
Izagirre also hinted at Movistar and Nairo Quintana's form going into the much anticipated Blockhaus stage.
"The whole team is delivering so far, everyone has seen it during this week. We've more than fulfilled the goal we had our minds on before starting the race, which was keeping (Quintana) out of trouble and in contention until the Blockhaus ascent.
"Now it's another completely different Giro, and we could see some interesting things already on Sunday."
Runner-up Visconti could not hide his disappointment with missing out on the win.
"Too bad the crash of Conti because I was forced to almost stop and restart. I feel sorry because I believe that I could win today, but I'm satisfied anyway," the Bahrain Merida rider said.
Race leader Bob Jungels crashed earlier on in the stage but safely finished with the bunch.
"The crash was my fault, because I didn't pay attention in the downhill," he said. "I touched the back wheel of a teammate and went down. Fortunately, it wasn't bad and at the moment I don't have too much pain, but we have to wait until tomorrow to see how I will feel."
