Jason Donohue's team had previously beaten the same opponent on Tuesday and Kevin Zefi netted his second in successive games after Rocco Vata had opened the scoring.
Ireland fell behind early on when Poland pounced from a corner kick on six minutes but that did not put the boys in green off their rhythm as they continued to play slick, attacking football.
On 44 minutes, the home side had a penalty that was saved by the Polish keeper but Vata was first to react and slotted in from close range to level the scores.
It was from another set-piece that Ireland profited when, on 64 minutes, Zefi found himself in the right place to fire in from around 22 yards out.
Ireland held onto the lead to wrap up a deserved win and complete a worthwhile test against good opposition.
Republic of Ireland: O'Leary; Heffernan, Curtis, Hughes (O'Brien 46), Kelly; O'Brien Whitmarsh (Murphy 47), Vata (Ferizaj 70), Barrett (Tettah 73); Zefi, Nugent (McLoughlin 55), Nolan (McManus 58).