The result means the Women's National League Champions sit in second spot in Group 10, with their final group game on Tuesday against Maltese side Birkirkara.
The hosts went ahead with a quarter of an hour gone through Isadora Freitas' header but Youths grew in confidence throughout the contest and were level in the 37th minute.
Rianna Jarrett burst down the right and found a pinpoint cross for McKenna Davidson to send a bullet header past Gintra goalkeeper Greta Lukjančukė to equalise.
Two minutes after the break, Youths were ahead. McKenna Davidson turned provider as her cross from the edge of the area on the left was met by the head of Lauren Kelly and she powered her header home off the post.
Wexford continued to create chances and could have been further ahead as Jarrett's late 25-yard effort was well saved by the keeper. It was deserved victory for Tom Elmes' side who praised the effort of the players after the match.
"It's a fantastic result for us and it was fully deserved," said manager Tom Elmes.
"The team really stuck to the game-plan and it worked well out to a tee, it was one of those games when it all came together. We've got great experience in the team but we're always bringing in new players and they've all brought into the ethos, and coming into European competition, maybe that's what we needed for everyone to gel together.
"I think you can see what we're capable of and we need to bring that into our domestic campaign when we return. We've got a big game on Tuesday and we want to finish as high as we can."
Wexford Youths: Williams (GK), Conlon (Rossiter 37), Dwyer, Murphy, Kennedy, Kelly, Davidson (Kingsley 83), Craven, Frawley (Parrock 90), Sinnott, Jarrett.
Yellow card(s): Murphy, Williams.