Shelbourne striker Leanne Kiernan opened the scoring mid-way through the second-half before Slovakia equalised through a Marie Hourihan own goal. However, substitute Amber Barrett fired home with three minutes remaining with Ireland set to host the European Champions the Netherlands on Tuesday.
A windswept Tallaght Stadium made chances few and far between during the first 45 minutes as captain Katie McCabe came closest with a header over the bar in the 23rd minute.
Roared on by a fantastic 3521 crowd at Tallaght Stadium, the WNT were much improved in the second-half and their mounting pressure saw the home side take the lead. With just over 20 minutes remaining, Cavan-native Kiernan was able to collect the ball before she turned her defender and fired the ball home.
Three minutes later, spirits were dampened as goalkeeper Marie Hourihan scored an unfortunate own goal but Colin Bell's side continued to press forward and wouldn't be denied.
Substitute Amber Barrett latched onto a Karen Duggan lofted-ball forward and found the bottom corner to cue wild scenes as Ireland secured a vital win.
Republic of Ireland WNT Head Coach Colin Bell said: "We're delighted to come away with the victory in the end. It was a difficult game and you've got to give credit to the opposition who defended well.
"Two fantastic goals from two home-based players which I think says a lot about how the game is growing here in Ireland and producing the talent we need for the international stage.
"I'd like to thank all of the supporters who turned up to support the team today. They really drove the team on in the final stages and helped us get those three points."
Republic of Ireland: Hourihan (GK), Perry, Caldwell, Quinn, Duggan, Fahey, Connolly, O'Sullivan, McCabe (C), Littlejohn (Barrett 77), Kiernan.