After scoring a hat-trick on Sunday, substitute Sean Kennedy was a hero yet again as his goal seven minutes from the final whistle proved decisive in separating the teams.
The game started quietly with chances few and far between in the opening 40 minutes.
The best chance of the half fell to Marc Walsh but unfortunately for the winger, his header was pushed over by Auron Loxha on the Kosovo line.
Albin Prapashtica was a constant danger for the visitors but tenacious tackling and a solid defence at both ends meant that something special was required to break the deadlock.
After the game remained scoreless at the interval, Prapashtica struck first in the second half. His low shot in the 44th minute was hit with such precision that Sean Bohan was left with no chance of getting a hand to it.
Heads remained high though and an audacious run from Ross Tierney six minutes later culminated in the midfielder being tripped inside the box.
Troy Parrott stepped up to the spot and converted by sending the ball straight down the middle.
Further attempts from Adonis Aliu and Barry Coffey were saved before Kennedy got a vital touch from a cross at the back post to hand his side the win.
Paul Osam's side now face Denmark in their final game of the tournament on Thursday as they attempt to leave Mayo with a clean sweep of victories.
Republic of Ireland: Sean Bohan, Conor O'Reilly (Max Murphy, 55), Oisin McEntee (Andrew Spain, 40), Cian Trehy, Aaron Mulligan, Ross Tierney, Jason Knight (Barry Coffey, 40), Marc Walsh (Sean Kennedy, 55), Conor Grant (Ciaran Brennan, 73), Matthew Everitt (Sean Mahon, 55), Troy Parrott.
Kosovo: Auron Loxha, Ermir Shabani (Edin Hyseini, 58), Leutrim Ismajlaj (Gentrit Olluri, 71), Dorian Osmanollaj, Leard Sadriu, Adonis Aliu (Robert Rahmani, 58), Florian Hysenaj (Gent Musa, 71), Blendi Morina (Hajdin Salihu, 73), Bajrush Osmani (Armend Gashi, 40), Arton Tolaj (Muhamet Hyseni, 40), Albin Prapashtica (Endrit Demolli, 71).
Referee: Chris Campbell.