Goals from Danny McGrath and Gabriel Gartside-Kelly secured the impressive victory, despite a late strike from Ágeir Galdur Guõmundsson, as Paul Osam's side finish their season on a high.
Ireland came into the game on the back of defeats to Switzerland and Sweden, despite a much-improved performance against the host nation, Sweden, whilst Iceland had secured two victories against the same opposition.
Ireland started the game strongly and should have taken the lead in the 10th minute. Gabriel Kelly was able to switch the ball from left to right to find Najemedine Razi but his powerful effort was well saved.
It didn't take Ireland long after that to take the lead. Mason Melia and Razi combined brilliantly on the edge of the area to see Melia in on goal and after he was taken down by the keeper, the referee awarded a penalty to Ireland.
Danny McGrath stepped up and made no mistake from 12 yards to give Ireland the lead. Ireland continued to pressure after the half-time break and doubled their lead with an incredible strike.
Gabriel Gartside-Kelly won the ball on the edge of the area and after he controlled, he produced a wonderful curling effort to the top right-hand corner in the 49th minute.
Ireland were able to control much of the second-half until the final moments when Iceland pulled one back in the 87th minute as Ágeir Galdur Guõmundsson pounced on the ball to find the net to make it a nervy ending to the fixture.
In the final minute of added time, a goal-mouth scramble saw two fantastic blocks from Stanley Ashbee and Gartside-Kelly keep Ireland ahead and secure the win to complete the UEFA Development Tournament in Sweden.
"The performance was really good and I thought we thoroughly deserved the victory. To come back from the defeat on Wednesday against Switzerland, a very disappointing and bizarre game, it is brilliant to come back from that. Iceland had won their two games coming into it so it was a big challenge for the players and staff, and delighted to get the win," said U-16 Head Coach Paul Osam.
"I thought we also didn't get what we deserved against Sweden either so we're licking our wounds, thinking is anything going to go for us, so that was important for the players and staff to get rewarded at the end of the season for them.
"We've developed throughout the week and that's been great to see. You want to win matches, of course, but the biggest thing is that the players are learning and developing and we've really seen them take that on board and work hard to improve.
"We had to put our bodies on the line at the end to get the win, that's in our DNA. Sometimes we can lose sight of that so we spoke about that before the game because we might have conceded goals previously where you'd expect them to be throwing their bodies on the line.
"Today, certainly, we weren't going to lose the game. I just felt they approached the game in the right way and that's a victory to finish off the season for them which is a huge boost."
Republic of Ireland: Jason Healy (GK), Sean Mackey, Corey O'Sullivan (Luke Nolan 64), Stanley Ashbee, Sean Hayden, Danny McGrath, Najemedine Razi (Taylor Mooney 80), Gabriel Gartside-Kelly, Luke Kehir (John O'Sullivan 64), Mason Melia (Romeo Akachukwu 80), Nickson Ebigualor Okosun (Shane Tracey 64).
Iceland: Ivar Ambro Porhallson (GK), Porri Stefan Porbjörnsson, Stigur Diljan Pórõarson, Daniel Tristan Guõjohnsen (C), Hrafn Guõmundsson, Ágeir Galdur Guõmundsson, Magnús Arnar Pétursson, Allan Purisevic, Óli Melander, Karl Ágúst Karlsson, Stefán Gisli Stefánsson.
Referee: Abdinaser Bashir (Sweden)
Ireland Goals: Danny McGrath (20 pen), Gabriel Gartside-Kelly (53)
Results - UEFA Development Tournament
11/05 - Switzerland 0-7 Republic of Ireland
13/05 - Sweden 2-1 Republic of Ireland
16/05 - Republic of Ireland 2-1 Iceland