Vera Pauw's team went in scoreless at half-time and fell behind soon after the restart when Paulina Dudek converted a penalty - harshly awarded for a handball against Niamh Fahey.
Ireland showed their fighting spirit with Lucy Quinn firing in a superb left-footed effort to draw level on 52 minutes before Louise Quinn powered in a header on 75 minutes to give them a lead that they would not surrender.
In what was a physical battle, Ireland went toe to toe with a team ahead of them in the FIFA Women's World Rankings and created several patterns of play that showed they are a team constantly trying to play on the front foot.
Fahey, making her 100th appearance, was immense as part of a back three alongside Louise Quinn and Savannah McCarthy. She didn't need the captain's armband to prove that she is a natural leader.
Denise O'Sullivan had the first chance of the game when she broke in behind the Polish lines inside the opening 15 minutes but her shot was directly at goalkeeper Karolina Kalbs.
Poland were given a penalty five minutes into the second half and Dudek made no mistake from the spot to give them the lead.
Ireland never panicked and continued to play in a positive way with Lucy Quinn cutting in from the right to wreak havoc while the composed passing of Ruesha Littlejohn linked play.
It was Birmingham City ace Lucy Quinn - who was the Sky Ireland Player of the Match - who got them back level when instinctively letting rip with her left foot from distance.
Poland had a couple of half chances, while O'Sullivan forced Kalbs into another save before Louise Quinn got her 13th senior goal with a header inside the penalty area after connecting with Katie McCabe's cross.
Wearing orange for the first time, Ireland held on to secure victory.
Ireland will next be in action on Saturday as they continue to use this tournament for preparation for the FIFA Women's World Cup Qualifier against Sweden in April.
Republic of Ireland: Courtney Brosnan; Niamh Fahey, Louise Quinn, Savannah McCarthy; Heather Payne (Jess Ziu 53), Ruesha Littlejohn, Megan Connolly, Katie McCabe; Lucy Quinn, Denise O'Sullivan; Kyra Carusa (Amber Barrett 82).
Poland: Karolina Kalbs; Martyną Wiankowska, Gabriela Grzywinska, Paulina Dudek, Małgorzata Mesjasz; Weronika Zawistowska, Ewelina Kamczyk, Dominika Grabowska, Zofia Buisewiska, Nikola Karczewska; Adriana Achinska.
Referee: Valentová Zuzana.
2022 Pinatar Cup Fixtures
Match A1 | Wales 3-1 Scotland, Pinatar Arena, KO 15:30 (14:30 Irish Time)
Match A2 | Slovakia v Belgium, Pinatar Arena, KO 20:30 (19:30 Irish Time)
Match B1 | Republic of Ireland 2-1 Poland, La Manga, KO 15:30 (14:30 Irish Time)
Match B2 | Hungary v Russia, La Manga, KO 20:30 (19:30 Irish Time)
A3 | Winner A1 v Winner A2, Pinatar Arena, KO 20:30 (19:30 Irish Time)
A4 | Runner-up A2 v Runner-up A1, Pinatar Arena, KO 15:30 (14:30 Irish Time)
B3 | Winner B2 v Winner B1, La Manga, KO 20:30 (19:30 Irish Time)
B4 | Runner-up B2 v Runner-up B1, La Manga, KO 15:30 (14:30 Irish Time)
Final | Winner A3 v Winner B3, Pinatar Arena, KO 20:30 (19:30 Irish Time)
3rd Place | Runner-up A3 v Runner-up B3, La Manga, KO 20:30 (19:30 Irish Time)
5th Place | Winner A4 v Winner B4, Pinatar Arena, KO 15:30 (14:30 Irish Time)
7th Place | Runner-up A4 v Runner-up B4, La Manga, KO 15:30 (14:30 Irish Time)
*Republic of Ireland and Slovakia will not play each other due to being in the same FIFA Women’s World Cup Qualifying Group