The 27-year-old Basque, who rides for the Euskadi Basque Country-Murias team, soloed away from his companions in the last 25 kilometres and a massive effort saw him hold to a six-second lead on the line.
Jonathan Lastra ((Caja Rural-Seguros RGA)) was second, with Lawson Craddock (EF Education First) coming in third, both part of a chasing pack that finished six seconds behind.
Australian Damien Howson (Mitchelton-Scott), also in the break which formed with less than 10 kilometres raced, finished fourth.
“To win at La Vuelta, and furthermore close to home and with my family around, is a dream come true," Iturria said.
"Before I came to the race, when the selection was made, they asked me which stage I’d like to win, and I chose this one.
"I’m not a cyclist used to winning and to open my record at La Vuelta is a dream.
"I suffered a lot on the climbs. I was feeling good but I suffered more than usual with the accelerations. When I got to the front, [team manager] Jon Odriozola told me ‘Attack with all you got and go to the finish.’
"I listened to him and I opened a nice gap. I gave my all the whole time, pushing to be as fast as possible, finding strength I didn’t know I had. I wasn’t thinking of the gap, I focused on myself. And I won.
"I don’t have words for this. We’ll have to toast with champagne tonight.”
Primoz Roglic (Jumbo-Visma) safely rode to the finish with the peloton, over 18 minutes behind the winner, to retain La Roja on the eve of a tricky stage to Bilbao.
He remains one minute 52 seconds ahead of Alejandro Valverde (Movistar) and two minutes 11 seconds in front of Miguel Angel Lopez (Astana) in the general classification.
“It was a bit of a hard start but then it was a nice day and my team did a great job," Roglic said.
"Tony Martin is my roommate and a very strong guy. With Lennard [Hofstede], he’s here to pull on the flat whereas Sepp [Kuss] or George [Bennett] are climbing guys. Neilson [Powless] is an all-rounder, Robert [Gesink] is a strong guy also for the mountains.
"We’ve proven this is a big team already. I don’t think tomorrow’s stage is more dangerous than the high mountains. I don’t have any problem with short climbs. We need to be focused on the moment and do our best."
That stage is a hilly 171.4km from Circuito de Navarra consisting of three category three climbs before a dramatic final descent into the city centre of Bilbao.