Colin O'Brien's side came from a goal down at the break to produce a dynamic second-half display to run out comfortable winners in the end.
Sean Mahon had the game's first chance when he volleyed over from the edge of the box in the sixth minute after connecting with a Callum Thompson cross from the left.
Poland took the lead in the 11th minute when the impressive striker Bartosz Marchewka fired in a low strike from 12 yards out which beat the Irish keeper.
Five minutes into the second half Marchewka produced another dangerous strike which was well saved by home keeper Harry Clarke.
In the 59th minute Ireland drew level when captain Kameron Ledwidge rifled to the bottom corner from the edge of the box after a free-kick was laid off for him to shoot.
Two minutes later winger Marc Walsh won a penalty after a probing run and Ledwidge stepped up to fire home from the spot-kick.
In the 74th minute Walsh stamped his authority on the game when he finished off a lightening counter-attack with a brilliant finish from a tight angle to seal the win.
"We were very pleased with the players over the course of the two games they've played this week. They will have a much better understanding of what is required at underage international level after these fixtures," said O'Brien.
"We will be looking at some more players next month and will have some assessments in the Christmas break then look towards our next international fixtures in the New Year."
REPUBLIC OF IRELAND: Harry Clarke, Ray O'Sullivan, Kameron Ledwidge, Callum Thompson, Barry Coffey, Adam O'Reilly, Sean Mahon, Kevin O'Reilly, Tony Mambouana, Oisin McEntee, Marc Walsh. Subs: Caelin Rooney for Thompson 40 mins; Sean Brennan for Coffey 40; Adam Idah for Mambouana 60; Jason Knight for Mahon 75.