The Hale brothers, Rory and Ronan, scored either side of Ryan Manning's first-half strike to make it a night to remember for the Derry City footballers.
It only took 14 seconds for Ireland to score the opener. Straight from kick-off, Joe Quigley knocked the ball down for Derry City forward Ronan Curtis and he found Rory Hale, who turned and slid the ball home.
Ireland continued to dominate the first-half as Josh Cullen fired over from 20 yards out and Ryan Manning saw his low 25-yard free-kick palmed away just past the half-hour.
Five minutes from the break, Manning doubled Ireland's lead. The QPR man won the ball back and played a neat one-two with Curtis to fire home over the keeper.
Iceland pulled a goal back in the 67th minute through Stefan Ljubicic who produced a curling finish off-the-post as Ireland made a number of changes during the second-half. Jake Doyle Hayes, James Dunne and Ronan Hale all came on for their U21 debut ahead of Tuesday's qualifier.
In the final minute, the latter marked his debut with a goal. The Icelandic keeper Aron Fridriksson could only clear the ball as far as Hale who found the net from 40 yards with a spectacular finish.
Republic of Ireland U21 Head Coach Noel King said: "We're really happy with the performance. We scored some great goals and seeing how many changes we made, it shows a great strength and depth in the squad.
"We let them come on to us during the second-half but I thought we managed it well and deserved the victory. It is great preparation for us going into Tuesday's game. We need to perform to those levels once again to get an important three points."
Republic of Ireland: Liam Bossin (GK), Liam Kinsella, Danny Kane (Jake Doyle Hayes 85), Ryan Sweeney (Ryan Delaney 46) Corey Whelan (James Dunne 72), Josh Cullen, Connor Dimaio, Joe Quigley (Ronan Hale 68), Ryan Manning, Ronan Curtis, Rory Hale (Olamide Shodipo 46).
Subs not used: Caoimhin Kelleher (GK).