Izaguirre spent most of the day in the lead group and broke away on the final sharp climb of the mainly uphill 173-kilometre course from Limone sul Garda to Pfalzen.
He finished in four hours two minutes to beat Alessandro De Marchi and Stef Clement by 16 seconds.
"It's true that it was a good finish today, which was well within my capability," Rodriguez said. "But you mustn't get carried away, there are still a lot of difficulties before we get to Milan next Sunday. I have to preserve myself and keep my energy for the days to come."
It was Izaguirre's first win on a grand tour. Rodriguez and Hesjedal finished 8:57 behind.
Izaguirre, De Marchi and Clement were among a group of riders that broke away about 70 kilometres into the stage, and swiftly established a lead of six minutes.
The lead was eventually extended to 12:30 as the peloton took it easy since no rider in the breakaway group was a threat to the overall leader. The highest-placed rider in the leading group was Jose Herrada, and he had been 32:26 behind Rodriguez at the start of the 16th stage.
Herrada attacked with just under five kilometres to go, on the short climb to Chienes, which has an average gradient at nine per cent, and a maximum of 12.
He was swiftly overtaken by Izaguirre and De Marchi. The Spaniard then opened up a gap on the rest of the leaders, and the Euskaltel rider sprinted clear down the final 200-yard straight to the line.
Hesjedal, a 31-year-old from Victoria, is the designated leader of the Garmin-Barracuda team. He has had two stints in the leader's pink jersey.
Dominique Rollin of Boucherville, Que., was 80th on the day and 126th overall. Christian Meier of Sussex, N.B., finished 134th on the stage and was 135th overall.
Svein Tuft of Langley, B.C., finished 143rd on the day and was 161st overall. Tuft and Meier ride for Australia's GreenEdge team while Rollin is with the French FDJ team.
Wednesday's 17th stage sends the peloton to the Dolomites mountain range. The 116-mile route features four tough climbs before the final descent into Cortina d'Ampezzo.
"I'm ready," Rodriquez said. "I know that it will be tough and I've prepared myself for it. We will know a bit more about everyone's assets, even though I don't think the Giro will play out only on this stage.
"It will be an important day but not decisive. There will be the chance to win some time but not to eliminate rivals."
The Giro ends Sunday in Milan.
With files from The Canadian Press.