All three goals came after the break as Shamrock Rovers' Ben Curtis and Bohemians duo Cian Kelly and Evan Ferguson scored for Jason Donohue's side.
The victory rounds off a successful week for the U-15s, who have remained undefeated in normal time in the international tournament. Ireland drew against Netherlands and Spain earlier in the week - losing on penalties on both occasions.
Ireland were on top throughout the first half and it was Finn Harps' Conor Campbell who went closest, but his low, powerful strike was palmed away by the Hungarian keeper Matyas Kiraly.
Ireland's dominance continued after the interval and they took the lead early into the second-half. In a move straight off the training ground, Curtis found the back of the net after a well-worked short corner in the 43rd minute.
Ireland doubled their lead with a classy counter-attack strike. Hungary failed to deal with the pace of the attack and Kelly notched his third goal of the week with a superb half-volley in the 55th minute.
In the final minute of the game, Ireland, who saw 19 of the 20-player squad play in today's game, added a third goal through substitute Ferguson. He rose highest to flick in a right-sided free-kick to record an impressive victory to end the tournament.
"It's a fantastic victory for the players who deserve tremendous credit for their efforts throughout the week," said U-15 Head Coach Donohue.
"We set a goal before the game to treat this like a qualification scenario and that we needed a 3-0 victory to qualify for the next tournament. The players were really pushing in the end to get that third goal so it's great for their education as it's important they learn about qualifying for tournaments for when they get older.
"The players have been well organised throughout the week and performed excellently in every match. Spain are the best U15 side I've ever seen and we matched them in normal time so it shows that there is some talent in the group.
"I want to thank all of the staff for their hard work throughout the week and the work continues when we return. We've got on-going assessments ahead of the next game against Cyprus in March."
Republic of Ireland: Aaron Maguire, Tommy Fogerty (Aaron O'Reilly 61), John Ryan (C) (Craig King 61), Ben Curtis (Glory Nzingo 53), Luke McGlynn, Conor Campbell (Cian Kelly 36), Michael Leddy (Ciaran O'Sullivan 53), John Joe Power (Jamie Mullins 53), Darragh Reilly (Edwin Agabje 53), Ben Quinn (Evan Ferguson 53), Sean Grehan.
Hungary: Matyas Kiraly, Dominik Kovacs, Bendeguiz Farkas (C), Istvan Pekar, Engelbert Folding, Zsombor Gruber (Dominik Kocsis 36), Noel Keresztes (Akos Tarcson 55), Renato Ulbert, Laszlo Kiss, Kevin Molnar (Balazs Bakti 55), Zoltan Vasvari (Daniel Nagy Kolozsvari 36).
Referee: Marcos Navarro Quinonero (Spain).
Results - International U15 Tournament
30/1: Republic of Ireland 1-1 Spain (1-4 pens), Pinatar Arena
1/2: Republic of Ireland 2-2 Netherlands (2-4 pens), Pinatar Arena
3/2: Republic of Ireland 2-0 Hungary, Pinatar Arena