It was a first victory in his maiden Grand Tour for the 23-year-old rider, who made his decisive move inside the final four kilometres of the 173km stage from Limone on the banks of Lake Garda.
Italian Alessandro De Marchi (Androni Giocattoli) led Dutchman Stef Clement (Rabobank) over the line to take second place, 16 seconds down on Izagirre.
Joaquim Rodriguez (Katusha) retained the leader’s pink jersey after the Spaniard arrived safely in a splintered peloton alongside his main rivals almost nine minutes in arrears.
With just a couple of minor unclassified climbs on the schedule, Tuesday’s stage always threatened to be a transitional affair – and once a group of 10 riders broke clear after 60km on the road, the Katusha team of Rodriguez was happy to let the gap grow to almost 13 minutes.
There was little action within the 10-man leading group, who combined well as the road climbed gradually upwards after the feeding zone half-way through the stage.
Spaniard Jose Herrada of Movistar was the best-placed of the escapees in the GC – just over half an hour down on compatriot Rodriguez.
It was Herrada who made the first move when the leaders reached the foot of the final ascent, 4.5km from the finish. His dig was checked by the rest of the group before Izagirre countered on a cobbled section of road.
De Marchi was the first to respond to Izagirre but soon crumbled, dropping back to ride alongside Herrada and Mathias Frank of BMC.
Herrada led the chase around a series of hairpin bends, but Izagirre continued to ride with experience beyond his tender years. The Euskaltel youngster held a lead of 14 seconds as the road flattened out inside the final 2km.
Rabobank’s Clement, part of the 10-man break, returned to the wheels of Herrada and De Marchi to help with the chase, but the trio had left it too late and Izagirre had the luxury of being able to sit up and savour his first major win in his maiden Grand Tour.
His head in his hands, Izagirre crossed the line 16 seconds clear of an irate De Marchi, who missed out in similar circumstances in Saturday’s stage 14, in which he finished third after losing out to Movistar’s Andrey Amador.
Clement finished just behind De Marchi, while Frank rolled home three seconds further back to take fourth, with Herrada taking fifth at 21 seconds.
Izagirre's victory came a month after the second-year pro notched his first professional win of his career - in the time trial at the Vuelta a Asturias.
The remaining five riders from the break – including stage 12 winner Lars Bak of Lotto Belisol – came home within 48 seconds of the winner Izagirre, before Team Sky’s Juan Antonio Flecha crossed the line 8:54 down to bring in the peloton.
The Liquigas team of Ivan Basso had set a fast pace at the start of the climb, but ultimately the ascent became a battle of attrition as the favourites for the GC seemed happy to take another day off ahead of Wednesday’s return to the high mountains.
The race will enter the Dolomites for stage 17 to Cortina d’Ampezzo with Rodriguez holding a 30 second lead over Canadian Ryder Hesjedal (Garmin-Barracuda), with Basso in third at 1:22.